CN101247376A - OFDM Channel Estimation Method Combined with Wavelet Transform Domain Denoising - Google Patents

Abstract

A method for estimating an OFDM channel in conjunction with wavelet transform domain denoising, comprising the steps of: extracting information on the pilot subcarrier, calculating the channel frequency response at the pilot subcarrier; according to the calculated channel frequency response at the pilot position, Interpolating the channel frequency response in the time direction; performing noise and interference removal on the interpolated channel frequency response in the time direction; performing interpolation in the frequency direction on the channel frequency response from which the noise and interference have been removed. Because noise, inter-subcarrier interference and linear interpolation will introduce errors into the channel frequency response value obtained by interpolation, these errors will cause the degradation of OFDM (Orthogonal Frequency Division Multiplexing) receiver performance. However, the above-mentioned method based on wavelet transform domain denoising can reduce the error introduced in the channel frequency response value, improve the accuracy of the channel estimation value, and reduce the bit error rate of the receiving system.

Description

OFDM Channel Estimation Method Combined with Wavelet Transform Domain Denoising

technical field

The present invention relates to a radio broadcasting system, in particular to an OFDM (orthogonal frequency division multiplexing) channel estimation method combined with wavelet transform domain denoising.

Background technique

DRM (Digital Radio Globalization) is the only universal non-proprietary digital radio broadcasting system for the shortwave, mediumwave and longwave AM broadcasting bands. Under the same coverage conditions, the power of the DRM (Digital Radio Globalization) transmitter is 6-9dB lower than that of the traditional analog transmitter, and the same-adjacent frequency protection rate of digital broadcasting is lower than that of analog broadcasting, and the ability to resist multipath interference is strong. It is convenient for mobile reception; the sound quality can reach the quality of CD (CD) or FM stereo; it can provide additional data and multimedia information; compared with DAB (Digital Audio Broadcasting), its receiver price is easier to be accepted by the audience. Its appearance is a sign of the revival of broadcasting in the frequency band below 30MHz, and it has now become an international standard.

In a coherent demodulation OFDM (Orthogonal Frequency Division Multiplexing) system, in order to equalize the received signal, the receiver must obtain channel amplitude and phase information through channel estimation. However, the broadcast channel not only suffers from frequency-selective fading caused by multipath propagation, but also suffers from time-selective fading caused by Doppler frequency shift or Doppler spread. In order to ensure the receiving quality and real-time performance of the receiver, The receiver is required to perform timely and accurate channel estimation on the broadcast channel. According to the requirements of the DRM (Digital Radio Globalization) specification, the transmitter sends the pilot data at the same time as the useful data, so that a channel estimation scheme based on the pilot can be adopted. First, extract the received signal at the pilot position, use the local pilot stored in the receiver, use the least squares algorithm to calculate the channel frequency response of the pilot position, and then use the interpolation filter to estimate the channel frequency response at the data subcarrier , and finally, equalize the received receipt with a single-tap frequency-domain equalizer. When the transmitted signal adopts high-order modulation, such as 16QAM (16 constellation point quadrature amplitude modulation) or 64QAM (64 constellation point quadrature amplitude modulation), in order to obtain better receiver performance, more accurate channel estimation is required.

Because under the condition of double-fading channel, that is, under the channel condition of both frequency selective fading caused by multi-path propagation and time selective fading caused by Doppler frequency shift or Doppler spread, the rhombic derivative The frequency pattern has better anti-fading characteristics than the block pilot pattern or the comb pilot pattern. This kind of time-frequency two-dimensional diamond pilot pattern is adopted in the DRM (Digital Radio Globalization) specification. This scheme can Reduced receiver performance degradation in cases where some pilots are heavily influenced by the channel. The diamond-shaped pilot pattern distribution diagram is shown in Fig. 1 .

For different channel conditions, the DRM (Digital Radio Globalization) standard includes four different robust modes, the specific description is shown in Table 1:

Table 1: Robust modes and corresponding channel conditions

Robust Mode channel conditions Mode A Gaussian channel, slight drop channel, suitable for mid-wave and long-wave channels during the day. Mode B Time- and frequency-selective channels, extended night-time SW and MW channels with longer delays. Mode C Time and frequency selective channels, poor channel conditions, large Doppler spread HF channels. Mode D Very robust mode, but suffers from data transfer rate due to too tight pilot spacing.

Different robust modes have different pilot intervals in the time direction and frequency direction, and the specific intervals are shown in Table 2:

Table 2: Pilot interval size

Robust Mode _NT N _F A 5 20 B 3 6 C 2 4 D 3 3

In Table 2, _NT and _NF represent the pilot interval in the time direction and the pilot interval in the frequency direction, respectively.

The first three robust modes can satisfy most DRM (Digital Radio Globalization) broadcasting applications. For mode A, it is not suitable for short-wave broadcasting due to the shorter guard interval and narrower subcarrier spacing. Only mode D is applicable to channel model 6 in the specification. This channel model not only has a long time delay spread, but also has a large Doppler spread. It is an approximate simulation of shortwave propagation in the equatorial region.

As we all know, the best channel estimator under the minimum mean square error criterion is the two-dimensional Wiener filter, but the two-dimensional Wiener filter is not easy to implement in practical engineering applications, but when the channel is a generalized stationary non-correlated scattering channel , two cascaded one-dimensional filters are a good choice. Interpolation in the time direction can be performed first, followed by interpolation in the frequency direction, or interpolation in the frequency direction can be performed first, followed by interpolation in the time direction. In Figure 2 we give a block diagram of two cascaded one-dimensional interpolation filters (first in the time direction and then in the frequency direction):

For pilot-assisted OFDM (Orthogonal Frequency Division Multiplexing) systems, the usual channel estimation method is to first use the least squares algorithm to obtain the channel frequency response of the pilot position, and then use two cascaded one-dimensional filters to The channel frequency response of the data position is estimated, for example: first simple linear interpolation in the time direction, and then linear interpolation in the frequency direction.

How to improve the performance of a pilot-based channel estimation method using linear interpolation in both time-frequency two-dimensional directions. As we know, due to noise, inter-subcarrier interference and linear interpolation, errors will be introduced in our final interpolated channel frequency response values, and these errors will cause performance degradation of OFDM (Orthogonal Frequency Division Multiplexing) receivers.

Contents of the invention

The purpose of the present invention is to provide an OFDM channel estimation method combined with wavelet transform domain denoising.

In order to achieve the above object, a kind of OFDM channel estimation method combined with wavelet transform domain denoising comprises steps:

a) extract the information on the pilot subcarrier, and calculate the channel frequency response at the pilot subcarrier;

b) interpolating the channel frequency response in the time direction according to the calculated channel frequency response at the pilot position;

c) performing noise and interference removal on the channel frequency response interpolated in the time direction;

d) Perform interpolation in the frequency direction on the channel frequency response from which noise and interference have been removed in the channel direction.

Because noise, inter-subcarrier interference and linear interpolation will introduce errors into the channel frequency response value obtained by interpolation, these errors will cause the degradation of OFDM (Orthogonal Frequency Division Multiplexing) receiver performance. However, the above-mentioned method based on wavelet transform domain denoising can reduce the error introduced in the channel frequency response value, improve the accuracy of the channel estimation value, and reduce the bit error rate of the receiving system.

Description of drawings

Fig. 1 is a diamond-shaped pilot pattern distribution diagram;

Fig. 2 is a block diagram of two cascaded one-dimensional interpolation filters;

Fig. 3 is a block diagram of the cascade interpolation method with noise removal;

Fig. 4 is a block diagram of noise removal process;

Fig. 5 is a block diagram of wavelet decomposition;

Fig. 6 is a block diagram of wavelet reconstruction;

Fig. 7 is the bit error rate characteristic of channel 3;

FIG. 8 shows the bit error rate characteristics of channel 4.

Detailed ways

In order to eliminate the influence of noise and interference as mentioned above, we add a noise and interference removal process after the interpolation in the time direction, and then we perform interpolation in the frequency direction, the block diagram of which is shown in Figure 3. Because noise, inter-subcarrier interference and linear interpolation will introduce errors into the channel frequency response value obtained by interpolation, these errors will cause the degradation of OFDM (Orthogonal Frequency Division Multiplexing) receiver performance. The present invention introduces a noise removal process between the interpolator in the time direction and the interpolator in the frequency direction. The basic principle is to remove noise from the channel frequency response obtained by interpolation in the time direction through wavelet transform, thereby improving the accuracy of the interpolation in the frequency direction. To achieve the purpose of reducing the channel estimation error and reducing the bit error rate of the receiver under the same signal-to-noise ratio. The noise removal process in Figure 3 is shown in Figure 4.

After the inverse Fourier transform is performed on the channel frequency response at the pilot subcarrier, we obtain the sample value sequence of the time-domain channel impulse response. We can notice that in addition to useful channel amplitude and phase information, each sample point also contains noise and interference from adjacent subcarriers. These interferences and noises will cause errors between the channel frequency response we get through interpolation and its true value.

In order to improve the performance of DRM (Digital Radio Globalization) receiver, we use discrete-time wavelet transform to separate useful channel information from noise and interference components. In fact, discrete-time wavelet transform is equivalent to a filter bank, including high-pass filter and low-pass filter. The output sequence after the convolution of the input sequence and the low-pass filter is called the scale coefficient, and the input sequence and the high-pass filter The output after convolution is called wavelet coefficients. If we threshold the wavelet coefficients and keep the scale coefficients unchanged, and then reconstruct the thresholded wavelet coefficients and unprocessed scale coefficients through the reconstruction filter bank, we can get the noise and interference eliminated Enter the sequence. Finally, we perform Fourier transform on the reconstructed input sequence to obtain the channel impulse response on each pilot subcarrier after denoising, so as to achieve the purpose of improving the accuracy of channel estimation.

The above noise and interference removal process consists of five steps, which are described in detail as follows:

1) Inverse Fourier transform

Inverse Fourier transform is performed on the sequence formed by the channel frequency response on the pilot subcarrier to obtain the channel impulse response sample sequence in the time domain:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;kn</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Wherein, M is the number of pilot subcarriers in one OFDM (Orthogonal Frequency Division Multiplexing) symbol.

2) Wavelet decomposition

Here, we use Harr wavelet for decomposition and reconstruction. The filter bank based on Harr wavelet consists of a high-pass and a low-pass, and its low-pass filter coefficient is $f_L=\left[\begin{array}{cc}\frac{\sqrt{2}}{2}& \frac{\sqrt{2}}{2}\end{array}\right],$ The high-pass filter coefficients are $f_h=\left[\begin{array}{cc}-\frac{\sqrt{2}}{2}& \frac{\sqrt{2}}{2}\end{array}\right].$ The main purpose of this step is to transform the channel impulse response sample sequence with noise and interference into the wavelet domain. If h _{n, l} ^L and h _{n, l} ^H are used to represent the scale coefficient and wavelet coefficient, then the mathematical expression of wavelet decomposition can be expressed as follows:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Wherein, h _{k, l} , 0≤k<M represents the channel impulse response sample sequence, and M is the length of the channel impulse response sample sequence to be processed.

The wavelet decomposition is shown in Figure 5:

3) Thresholding

The main purpose of this process is to set all wavelet coefficients below a certain threshold to zero. Because among the wavelet coefficients after wavelet decomposition, the larger wavelet coefficients contain useful information, while the smaller wavelet coefficients mainly contain noise and interference components, so we can set the wavelet coefficients below a certain threshold to zero , so as to achieve the purpose of removing noise and interference.

There are three main threshold methods commonly used, they are hard threshold method, soft threshold method and non-negative threshold method, which are defined as follows:

${\stackrel{\&OverBar;}{h}}_{k,l}^h=\left\{\begin{array}{cc}0& \left|h_{k,l}^h\right|\&le;\mathrm{\&lambda;}\\ h_{k,l}^h& \left|h_{k,l}^h\right|>\mathrm{\&lambda;}\end{array}\right.$ (hard threshold) (4)

${\stackrel{\&OverBar;}{h}}_{k,l}^h=\left\{\begin{array}{cc}0& \left|h_{k,l}^h\right|\&le;\mathrm{\&lambda;}\\ h_{k,l}^h-\mathrm{\&lambda;}& h_{k,l}^h>\mathrm{\&lambda;}\\ h_{k,l}^h+\mathrm{\&lambda;}& h_{k,l}^h<-\mathrm{\&lambda;}\end{array}\right.$ (soft threshold) (5)

${\stackrel{\&OverBar;}{h}}_{k,l}^h=\left\{\begin{array}{cc}0& \left|h_{k,l}^h\right|\&le;\mathrm{\&lambda;}\\ h_{k,l}^h-{\mathrm{\&lambda;}}^2/h_{k,l}^h& \left|h_{k,l}^h\right|>\mathrm{\&lambda;}\end{array}\right.$ (non-negative threshold) (6)

Among them, λ represents the threshold, and λ≥0.

The method of removing noise and interference in the wavelet transform domain is different from the traditional method of denoising based on low-pass filter, because it adopts the threshold value processing process of wavelet coefficients, so it is nonlinear. Among them, the selection of the threshold is very important. Usually, selecting an appropriate threshold is an important prerequisite to ensure good noise and interference removal effect. If the threshold value is selected too large, some important and useful information will be filtered out. On the contrary, if the threshold value is selected too small, more interference and noise components will be included when we reconstruct, thus failing to achieve to the purpose of noise and interference removal. The empirical formula of the wavelet threshold proposed by Donoho is as follows:

$\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; log</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; /</span>\sqrt{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

This is just an empirical formula, not for all applications, the threshold selected according to this formula will have a good effect, usually, for different applications, we need to reselect the threshold suitable for this application, but the above Donoho experience The formula can provide us with a basic reference.

Many scholars have confirmed through research that, usually, the hard threshold method will introduce a large variance, while the soft threshold method will introduce a relatively large deviation. Considering the impact on variance and bias, some scholars also proposed a method combining soft threshold and hard threshold.

4) Wavelet reconstruction

The purpose of wavelet reconstruction is to transform the thresholded wavelet coefficients and unprocessed scale coefficients from the wavelet transform domain back to the time domain. This reconstruction is achieved by a reconstruction filter bank, which includes a high-pass and a low-pass, the coefficients of the low-pass filter and high-pass filter are respectively ${\tilde{f}}_L=\left[\begin{array}{cc}\frac{\sqrt{2}}{2}& \frac{\sqrt{2}}{2}\end{array}\right]$ and ${\tilde{f}}_h=\left[\begin{array}{cc}\frac{\sqrt{2}}{2}& -\frac{\sqrt{2}}{2}\end{array}\right].$ The reconstructed channel impulse response sample sequence It can be expressed as:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

是对原始的带有噪声和干扰的信道冲激响应样值输入序列h_k，l进行噪声和干扰去除之后的输出序列。

和

分别表示偶数和级数样点输出序列值。

is the output sequence after removing the noise and interference from the original channel impulse response sample input sequence h _{k, l} with noise and interference.

and

Represents the output sequence values of even and progressive samples, respectively.

The wavelet reconstruction process is shown in Figure 6.

5) Fourier transform

Transform the noise and interference-removed channel impulse response sequence to the frequency domain:

${\hat{h}}_{k,l}=\underset{\mathrm{no}=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\hat{h}}_{\mathrm{no},l}{e}^{-j2\mathrm{\&pi;nk}/m}$ 0≤k≤M-1 (10)

Wherein, M is the number of pilot subcarriers in an OFDM (Orthogonal Frequency Division Multiplexing) symbol, and the output sequence after Fourier transform can be used for interpolation in the frequency direction.

Example

The actual DRM (Digital Radio Globalization) broadcast channel is a double-fading channel with both frequency selectivity caused by multipath and time selectivity caused by Doppler spread or frequency shift. Among them, the multipath propagation is mainly caused by the reflection of the ionosphere at different heights. The maximum delay spread of the channel can reach several milliseconds. The Doppler spread and frequency shift are mainly caused by the spectral characteristics of the ionospheric reflection and the movement of the receiver. . Taking mid-latitude regions as an example, the maximum delay spread can reach 6ms, and the Doppler spread can reach 5Hz. Typically, the typical values of delay spread and Doppler spread are 2ms and 1Hz, which are the parameter values of the channel model 4 we use.

Based on the principle of proceeding from reality, we have investigated the situation of channel model 3 and channel model 4 in the DRM (Digital Radio Globalization) specification, in which channel model 3 is the US Consortium (United States Consortium) model for mid-frequency and high-frequency, Channel Model 4 is a standard CCIR (International Radio Commission) model for high frequencies. The specific parameters of channel model 3 and channel model 4 are given in Table 3 and Table 4 respectively:

Compared with the traditional linear interpolation method (linear interpolation in the time direction and frequency direction), the method combined with wavelet transform domain noise and interference removal has better bit error rate characteristics than the traditional method, which can be obtained from our It can be seen from the simulation results of channel model 3 and channel model 4, and the performance of combining the soft threshold method is better than that of combining the hard threshold method.

Table 3: Parameter settings for channel model 3

Path 1 path 2 path 3 path 4 Delay 0 0.7 milliseconds 1.5 milliseconds 2.2 milliseconds path gain 1 0.7 0.5 0.25 Doppler shift 0.1 Hz 0.2 Hz 0.5 Hz 1.0 Hz Doppler extension 0.1 Hz 0.5 Hz 1.0 Hz 2.0 Hz

Table 4: Parameter settings for channel model 4 path 1 path 2 Delay 0 2 milliseconds path gain 1 1 Doppler shift 0 0 Doppler extension 1 Hz 1 Hz

In our DRM (Digital Radio Globalization) simulator, we examine the traditional linear interpolation method and the hard threshold and soft threshold wavelet noise and interference removal methods in the frequency direction based on the same linear interpolation in the time direction performance. Among them, the hard threshold method is shown in formula (4), and the soft threshold method is a formula after adjusting formula (5), which is given by formula (11). The specific simulation parameters are shown in Table 5:

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}& \mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Table 5: Simulation parameter settings

Transmission mode B bandwidth 10K Mapping method 64QAM code rate 0.6 Channel model Channel 3 and Channel 4

The simulation results of channel model 3 and channel model 4 are shown in Fig. 7 and Fig. 8 respectively. From the simulation results, we can see that the method combined with hard threshold wavelet domain noise and interference removal is better than the traditional linear interpolation method, and the method combined with soft threshold wavelet domain noise and interference removal is better than the method combined with hard threshold.

For channel model 3, compared with the traditional linear interpolation method, the method combined with hard threshold has about 0.3-0.4dB gain, and the method combined with soft threshold has about 0.6-0.7dB gain; for channel model 4, Compared with the traditional linear interpolation method, the method combined with hard threshold has about 0.3dB gain, and the method combined with soft threshold has about 0.5-0.6dB gain.

Claims (8)

1. A method for estimating an OFDM channel in conjunction with wavelet transform domain denoising, comprising steps: a) extract the information on the pilot subcarrier, and calculate the channel frequency response at the pilot subcarrier; b) interpolating the channel frequency response in the time direction according to the calculated channel frequency response at the pilot position; c) performing noise and interference removal on the channel frequency response interpolated in the time direction; d) Perform interpolation in the frequency direction on the channel frequency response from which noise and interference have been removed in the channel direction. 2. method according to claim 1, is characterized in that described step c) comprises: Inverse Fourier transform is performed on the channel frequency response obtained by interpolation in the time direction; Perform wavelet decomposition; Do threshold processing; Perform wavelet reconstruction; Perform a Fourier transform to transform the processed data back into the frequency domain. 3. method according to claim 2, is characterized in that described wavelet decomposition adopts Harr wavelet decomposition. 4. method according to claim 3, it is characterized in that described Harr wavelet decomposition comprises high-pass filter and low-pass filter, wherein, the output after input sequence and low-pass filter convolution is called scale coefficient, The output after convolving the input sequence with a high-pass filter is called wavelet coefficients. 5. The method according to claim 2, wherein the threshold processing comprises one of a hard threshold method, a soft threshold method and a non-negative threshold method. 6. method according to claim 5, is characterized in that described threshold value is selected as follows: $\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; log</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; /</span>\sqrt{\mathrm{<span\; class="notranslate">\; N</span>}}$ Among them, λ represents the threshold, and λ≥0, σ represents the size of the noise, and N is the length of the data to be processed. 7. The method according to claim 6, characterized in that: selecting an appropriate threshold, setting all wavelet coefficients below a certain threshold to zero, and relatively large wavelet coefficients contain useful channel information. 8. The method according to claim 2, characterized in that the wavelet reconstruction transforms the thresholded wavelet coefficients and unprocessed scale coefficients back from the wavelet domain to a time threshold.

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