CN100452652C - Bi-orthogonal filter design method and its design device - Google Patents

Abstract

The device for designing dual orthogonal filter (DOF) includes following parts and operations: transmission filter (TF) design device in use for designing TF by using traditional method; FFT device in use to calculate FFT to calculate frequency response; device for selecting target correlation function in use for selecting target cross power spectrum function (TCPSF), and aliasing the function sampled in 1/Ts interval to obtain a constant; device for designing receiving filter carries out dividing TCPSF by frequency response of transmission filter in frequency domain (FD), or equivalent deconvolution operation in time domain (TD); adding window for the result, or equivalent convolution operation of window function in TD; inverse Fourier transforming the signal with window being added to TD, conjugated backout for the signal in TD so as to obtain impulse response in TD of DOF. Dual orthogonal nature between receiving filter and TF guarantees no loss on comm. system.

Description

A design method and device for biorthogonal filter

technical field

The invention relates to a design method of a bi-orthogonal filter and a design device thereof, in particular to a design method of a bi-orthogonal filter applied to a single carrier-frequency division multiple access system (SC-FDMA) and a design device thereof.

Background technique

The single-carrier-frequency-division multiple access system is a new type of frequency-division multiple access communication system that has not only the peak-to-average ratio of single-carrier communication power, but also has the characteristics of simple implementation of multi-carrier communication and flexible resource scheduling. It is mainly used in the uplink solution of broadband mobile communication, and supports frequency domain expansion technology, frequency domain equalization method and multi-user concurrent communication scenarios. In the single carrier-frequency division multiple access system, the entire broadband channel is divided into several orthogonal or quasi-orthogonal sub-channels on the frequency spectrum, and each user exclusively occupies a different sub-channel. On each sub-channel, user information is transmitted using a single carrier. In the transmitter of the single carrier-frequency division multiple access system, in order to reduce the inter-symbol interference (ISI) and ensure the orthogonality of each sub-channel spectrum, it is necessary to use a transmit filter to perform pulse shaping and spectrum shaping on the transmit pulse sequence. At the same time, in the receiver of the system, it is necessary to use a receiving filter corresponding to the transmitting filter to perform symbol timing and correlation reception on the received signal.

At present, the more common pulse shaping filters include: root raised cosine roll-off filter and Gaussian pulse shaping filter. The former uses the Nyquist technique to achieve a time-domain impulse response that is zero at the peak position of the adjacent symbol; the latter uses a Gaussian function to construct a transfer function that has a smooth transfer function, no zero-crossing point, and is strongly dependent on the 3dB bandwidth. However, both the root raised cosine roll-off filter and the Gaussian pulse shaping filter have obvious defects when applied in the uplink solution of the single carrier-frequency division multiple access system. Generally, in order to improve spectrum utilization and maintain orthogonality between sub-channels, the transmit low-pass filter needs to have faster attenuation in the frequency domain. For the root raised cosine roll-off filter, this requirement can be met by reducing the roll-off factor, but at the same time, with the decrease of the roll-off factor, the attenuation of the time domain response of the root raised cosine roll-off filter will be significantly slower. On the one hand, a longer time-domain pulse waveform will increase the truncation error of the filter, and on the other hand, it will greatly increase the processing complexity of the transmitting end, which is especially unfavorable for uplink transmission. Although the Gaussian filter is relatively concentrated in the time domain and has a short impulse response, its absolute bandwidth is much larger than that of the raised cosine filter, and it is difficult to meet the requirements of multi-user transmission for spectrum multiplexing.

On the other hand, when the traditional root-raised cosine roll-off filter and Gaussian pulse shaping filter are applied to the uplink solution of the single carrier-frequency division multiple access system, there is a contradiction that the time domain and the frequency domain cannot be "gathered" at the same time. When the filter can meet the fast attenuation in the frequency domain, that is, to ensure the orthogonality of the sub-channels, it cannot have a shorter time-domain impulse response, which cannot be realized with a smaller-order FIR filter, and the operational complexity of the transmitter It is very large; when the filter has a short time-domain response, the orthogonality between sub-channels cannot be well maintained in the frequency domain, resulting in a decrease in the spectrum utilization of the communication system.

Contents of the invention

The technical problem to be solved by the present invention is to provide a biorthogonal filter design method and its design device. Different filters can be designed at the transmitting end and receiving end of the communication system to process the signal. Under the conditions of domain orthogonality and peak-to-average ratio index, the time domain length of the transmitting filter can be greatly shortened, and the processing complexity of the transmitter is reduced; at the same time, the biorthogonal filter at the receiving end can achieve a performance equivalent to that of the matched filter. The shift orthogonality based on the symbol period ensures that there is no loss in the performance of the communication system.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A biorthogonal filter design method is provided, comprising the steps of:

Step 1, first design the transmit filter;

Step 2, calculating the transmit filter frequency response;

Step 3, select target cross power spectrum function, this function is a constant after aliasing with the sampling interval of 1/T _s ;

Step 4. Divide the target cross-power spectrum function R _tr [k] and the frequency response of the transmit filter H _t [k] in the frequency domain, or an equivalent time-domain deconvolution operation; Domain windowing or equivalent time domain window function convolution operation, the windowed signal is transformed into the time domain by inverse Fourier transform, and the time domain signal h′ _r [n] is conjugated in reverse order to obtain the received double positive The time-domain impulse response h _r [n] of the cross-filter.

Further, the design method in step 1 is a FIR filter design method.

The target cross-power spectrum function in step 3 is a raised cosine transfer function.

The target cross power spectrum function in step 3 satisfies: R _tr [k′]=K′, where K′ is a constant. R _tr [k′] is the target cross power spectrum function.

Further, the calculation formula in the step 4 is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; IFFT</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; win</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; IFFT</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; win</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span>}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span>\end{array}\right.$

Among them, R _tr [k] is the target cross power spectrum function, H _t [k] is the frequency response of the transmit filter, win[k] is the window function in the frequency domain, h _r [n] is the time domain of the receive filter Impulse response, h′ _r [n] and H′ _r [n] are intermediate variables.

Simultaneously, the present invention also provides a kind of biorthogonal filter design device, it is characterized in that, comprises:

A launch filter design device is used to design a launch filter using a traditional method;

The FFT transformation device performs FFT transformation to calculate the transmit filter frequency response;

The target correlation function selection device is used to select the target cross-power spectrum function, which becomes a constant after aliasing at a sampling interval of 1/T _s ;

The receiving filter design device is used to divide the target cross-power spectrum function R _tr [k] and the frequency response of the transmitting filter H _t [k] in the frequency domain, or the equivalent time-domain deconvolution operation, the obtained As a result, frequency-domain windowing or equivalent time-domain window function convolution operation is performed, and the windowed signal is transformed into the time domain by inverse Fourier transform, and the time-domain signal h′ _r [n] is conjugated in reverse order to obtain Time-domain impulse response h _r [n] of the receive biorthogonal filter.

Further, a transmit filter performance indication selection device is connected before the transmit filter design device, which is used to calculate the time-frequency design index of transmit filter according to the requirements of the actual communication system.

Further, a Fourier transform device is further provided between the target correlation function selection device and the receiving filter design device, and the target cross-power spectrum function is obtained in the frequency domain after Fourier transform is performed on the target correlation function.

The receiving filter and the transmitting filter of the present invention have good biorthogonal characteristics, and can achieve the shift orthogonality based on the symbol period equivalent to the matched filter, thereby ensuring that there is no loss in the performance of the communication system; at the same time, due to The order of the transmit filter can be controlled in a low range, and when it is applied to the solution of the uplink, the calculation load of the transmitter is greatly reduced. Theoretical analysis and simulation results show that the filter design scheme is easy to implement and feasible.

Description of drawings

Fig. 1 is the magnitude-frequency and phase-frequency response graph of the transmitting filter of the present invention.

Figure 2 is a statistical diagram of the peak-to-average ratio performance of the transmit filter.

Figure 3 is a time-domain impulse response diagram of the transmit filter and receive filter.

Fig. 4 is a graph of shifted orthogonality of the time-domain impulse responses of the transmit filter and the receive filter.

Figure 5 is the transmit and receive filter frequency domain responses and the target cross-power spectrum (partial) of two adjacent sub-bands.

Figure 6 shows the frequency domain responses of the transmit and receive filters and the target cross-power spectrum of two adjacent subbands.

FIG. 7 is a schematic structural diagram of a biorthogonal filter design device of the present invention.

Detailed ways

In a communication system, if the entire system response (including transmitter, channel and receiver) is designed to respond to the current symbol at each sampling moment at the receiver, while the response to other symbols is zero, then the inter-symbol The effect of interfering with the ISI can then be completely neutralized. This condition can be expressed mathematically as:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; K</span>}& \mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&PlusMinus;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&PlusMinus;</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&PlusMinus;</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\end{array}\right.<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>$

Among them, T _s is the symbol period, h _t is the time domain response of the transmit filter, h _r is the time domain response of the receive filter, R _tr is the output result of the correlation receiver, n is an integer, and K is a non-zero constant.

Since the transmit filter can be designed arbitrarily by using the traditional FIR filter design method according to the performance index required by the system, the biorthogonal filter design problem is: given h _t and constraints (1), solve h _r .

According to the relationship between correlation and convolution, formula (1) can be expressed in the following form (* indicates linear convolution):

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Transform formula (2) into frequency domain:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

At the same time, if the output result R _tr of the correlation receiver is resampled with T _s cycle, it can be obtained from formula (1):

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Transform equation (4) into the frequency domain:

R _tr [k']=K' (5)

From the derivation of formula (1) ~ formula (5), it can be seen that if the cross-power spectrum of the time-domain impulse response of the transmitting filter and the receiving filter is aliased at a sampling interval of 1/T _s , the result is a constant; Then the orthogonality of shifts between the transmit filter and the receive filter at intervals of symbol period T _s can be guaranteed. From formula (3) and formula (4), it is known that time domain correlation can be processed into the form of frequency domain multiplication. Therefore, as long as the cross-power spectrum function satisfying the above conditions is selected, the biorthogonal receiving filter corresponding to the known transmitting filter can be calculated by dividing the spectrum in the frequency domain.

In practical applications, the transfer function of the raised cosine roll-off filter can be selected to calculate the target cross power spectrum function, namely:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="1"\; label="s"\; filenames="C20061002403400112.png,C20061002403400121.png"\; state="\{\{state\}\}">s</figure-callout></span>}}\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="0"\; label="s"\; filenames="C20061002403400111.png,C20061002403400121.png"\; state="\{\{state\}\}">s</figure-callout></span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ></span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Therefore, the biorthogonal receive filter can be obtained by the spectral division method in the frequency domain at the same time. It is worth noting that: in the communication system, both R _tr and H _t are low-pass filters, so the division in the stop band range sometimes results in the division of two very small numbers resulting in a large amplitude . In order to avoid the distortion caused by this situation, it is necessary to perform a windowing operation on the spectral division result.

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; IFFT</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; win</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; IFFT</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; win</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span>}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span>\end{array}\right.<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>$

Among them, R _tr [k] is the target cross power spectrum function, H _t [k] is the frequency response of the transmit filter, win[k] is the window function in the frequency domain, h _r [n] is the time domain of the receive filter Impulse response, h′ _r [n] and h′ _r [n] are intermediate variables.

A multi-band filter bank-based orthogonal multiplexing multi-carrier uplink communication system (GMC-uplink) is used as the specific implementation environment of the present invention. Among them: the number of sub-bands is 16, the up-sampling multiple is 18, the frequency is 4.096MHz, and the sub-band bandwidth is 300KHz.

Biorthogonal filter design method of the present invention, comprises the steps:

Step 1. Calculate the time-frequency design index of the transmit filter according to the requirements of the actual communication system: the adjacent channel leakage ratio (Adjacent Channel Leakage Ratio, ACLR) indicates that the transmit power leaks to the first or second adjacent channel carrier power Numerical values, the sub-channel orthogonality requirements that need to be met in the transmit filter design in this specific embodiment are: ACLR ₁ <33dB ACLR ₂ <43dB. The specific design indicators are shown in the table below:

Design Method FIRLeast-squares Response Type Low pass Fs 4096000Hz Specify order 160 Fpass 125000Hz Wpass 0.7 Fstop 128000Hz Wstop 60

Step 2, utilize traditional method to design launch filter: call the filter design tool Filter Design&Analysis Tool in MATLAB 7.0 to design launch filter in this specific embodiment. The amplitude-frequency and phase-frequency responses of the transmitting filter are shown in Figure 1: it reflects the spectral performance and phase performance of the transmitting filter, and meets the design specifications.

When using QPSK modulation for 4 sub-band transmission, the peak-to-average ratio performance statistics of the transmit filter are shown in Figure 2: the peak-to-average ratio directly affects the power consumption of mobile phones, and only filters with PAPR that meet the requirements can be applied in wireless communication systems

in:

A total of 211,272 data blocks were counted, MAX(PAPR)<5.4

Step 3, select target cross power spectrum function, this function is a constant after the sampling interval aliasing of 1/T _s : select the transfer function of raised cosine roll-off filter as target correlation function in this specific embodiment, roll-off factor 0.15, 8 symbol periods are reserved before and after the peak value of the impulse response. The number of points of the FFT is 289 points.

Step 4. Divide the target cross-power spectrum function R _tr [k] and the frequency response of the transmit filter H _t [k] in the frequency domain, or an equivalent time-domain deconvolution operation; Domain windowing or equivalent time domain window function convolution operation, the signal after windowing is transformed into the time domain by inverse Fourier transform, and the time domain signal h _r ′[n] is conjugated in reverse order to obtain the received double positive The time-domain impulse response h _r [n] of the cross-filter.

Utilizing the method of the present invention, a dual-orthogonal receiving filter is designed with a filter order of 289. The performance of the filter is shown in Figures 3, 4, 5, and 6 below: it reflects that the receiving filter and the transmitting filter of the present invention have good biorthogonal characteristics, and can achieve a symbol-period-based Shifting orthogonality ensures that there is no loss in the performance of the communication system; at the same time, the processing complexity of the transmitter is greatly reduced due to the reduction of the transmit filter order.

Further, the present invention also provides a biorthogonal filter design device (as shown in Figure 7), comprising: a transmit filter performance index selection device 1, a transmit filter design device 2, an FFT (Fourier) transform A device 3 , an object correlation function selection device 4 , an FFT transformation device 5 , and a receiving filter design device 6 .

The transmit filter performance index selection device 1 calculates the time-frequency design index of the transmit filter according to the requirements of the actual communication system. For example cutoff frequency, passband gain, filter order. In order to reduce the computational complexity of the transmitter as much as possible, the order of the filter should be as low as possible. At the same time, the design index of the transmit filter needs to meet the requirements of the wireless communication system for peak-to-average ratio (PAPR). Since the biorthogonal filter proposed by the present invention can be widely used in different communication systems, different systems have different requirements on pulse shaping, spectrum shaping and peak-to-average ratio. The specific index can be obtained from the design definition of the communication system, and this device is the prior art and will not be repeated here.

A transmit filter design device 2 uses a traditional FIR digital filter design method to design a transmit filter that satisfies the output design index of the transmit filter performance selection device 1 . This design device is also the prior art and will not be repeated here.

The FFT transformation device 3 pads the end of the time-domain impulse response of the transmit filter designed by the device 1 with zeros, and then performs the FFT exchange of the K point. to obtain the transmit filter frequency response. The FFT transform dimension is equal to the length (order) of the time-domain impulse response of the receive filter.

The target correlation function selection device 4 selects a cross power spectrum function satisfying the condition described in formula (5), and the function becomes a constant after being aliased at an interval of 1/T _s . The transfer function (6) of the raised cosine roll-off filter is a special case that satisfies this condition, and different roll-off factors can be selected to control the spectrum shape as required. The variation range of the roll-off factor is from 0 to 1, and the smaller the roll-off factor, the faster the attenuation speed in the frequency domain. When the sub-channels are close to each other, the filter needs to attenuate quickly in the frequency domain, and the roll-off system should be reduced accordingly. In this specific embodiment, the roll-off factor is selected as 0.15.

The FFT transformation means 5 pads the end of the target correlation function selected by the target correlation function selection means 4 with zeros, and then performs the FFT transformation of the K point. The FFT transform dimension is equal to the length (order) of the time-domain impulse response of the receive filter.

The receiving filter design device 6 divides the frequency response of the transmitting filter and the target cross-power spectrum function to obtain the spectrum of the receiving biorthogonal filter, and performs windowing processing in the frequency domain, and then calculates the frequency spectrum of the receiving biorthogonal filter Time Domain Impulse Response.

Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these modifications and variations. For example, in step 4 of the present invention, an equivalent time-domain deconvolution operation can also be used; then the obtained result is subjected to an equivalent time-domain window function convolution operation, and the windowed signal is transformed into the time domain by inverse Fourier transform, The time-domain impulse response h _r [n] of the receiving biorthogonal filter is obtained after the conjugate inversion operation is performed on the time-domain signal h _{′ r} [n].

Claims (8)

1, a kind of biorthogonal filter design method is characterized in that, comprises the steps: Step 1, first design the transmit filter; Step 2, calculating the transmit filter frequency response; Step 3, select target cross power spectrum function, this function is a constant after aliasing with the sampling interval of 1/T _s ; Step 4. Divide the target cross-power spectrum function R _tr [k] and the frequency response of the transmit filter H _t [k] in the frequency domain, or an equivalent time-domain deconvolution operation; Domain windowing or equivalent time-domain window function convolution operation, the windowed signal is transformed into a time-domain signal h' _r [n] by inverse Fourier transform, and the time-domain signal h' _r [n] is conjugated The time-domain impulse response h _r [n] of the receiving biorthogonal filter is obtained after the reverse sequence operation. 2. The biorthogonal filter design method according to claim 1, wherein the design method in step 1 is a FIR filter design method. 3. The biorthogonal filter design method according to claim 1, wherein the target cross-power spectrum function in said step 3 satisfies: R _tr [k']=K', where K' is one constant, R _tr [k′] is the target cross power spectrum function. 4. The biorthogonal filter design method according to claim 1, wherein the calculation formula in the step 4 is: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; IFFT</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; win</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; IFFT</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; win</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span>}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ]</span>\end{array}\right.$ Among them, R _tr [k] is the target cross power spectrum function, H _t [k] is the frequency response of the transmit filter, win[k] is the window function in the frequency domain, h _r [n] is the time domain of the receive filter Impulse response, h _r ′[n] and H _r ′[n] are intermediate variables. 5. The biorthogonal filter design method according to claim 1, wherein the target cross power spectrum function is a transfer function of a raised cosine roll-off filter. 6. A biorthogonal filter design device, characterized in that it comprises: A transmitting filter design device is used to design a transmitting filter using a traditional method; The target correlation function selection device is used to select the target cross-power spectrum function, which becomes a constant after aliasing at a sampling interval of 1/T _s ; The receiving filter design device is used to divide the target cross-power spectrum function R _tr [k] and the frequency response of the transmitting filter H _t [k] in the frequency domain, or the equivalent time-domain deconvolution operation, the obtained As a result, frequency-domain windowing or equivalent time-domain window function convolution operation is performed, and the windowed signal is transformed into a time-domain signal h' _r [n] by inverse Fourier transform, and the time-domain signal h' _r [n] The time-domain impulse response h _r [n] of the receiving biorthogonal filter is obtained after the conjugate inversion operation; A first Fourier transform device, located between the transmit filter design device and the receive filter design device, for performing Fourier transform to calculate the frequency response of the transmit filter; A second Fourier transform device, located between the target correlation function selection device and the receiving filter design device, is used to perform Fourier transform on the target cross-power spectrum function. 7. The biorthogonal filter design device according to claim 6, wherein a transmit filter performance indication selection device is also connected before the transmit filter design device, which is used to calculate according to the requirements of the actual communication system The time-frequency design index of the emission filter. 8. The biorthogonal filter design device according to claim 7, characterized in that the FFT transform dimension of the Fourier transform device is equal to the time-domain impulse response length of the receiving filter.

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