CN116760414A - Method for converting sampling rate of arbitrary multiple in software radio system - Google Patents

Abstract

The invention discloses a method for converting sampling rate of arbitrary multiple in a software radio system, which belongs to the technical field of wireless communication and comprises the following steps: in the preparation stage, firstly, determining the signal segmentation length according to the symbol rate, determining the shortening length of a filter and a window function used for shortening according to the calculation amount requirement, and then calculating and storing the coefficient of a reconstruction filter corresponding to each new sampling moment and the old sampling moment corresponding to the input data of the filter; in the signal real-time processing stage, a known reconstruction filter coefficient is called to perform time-varying filtering operation on the input data under the old sampling rate, so as to obtain a signal under the new sampling rate. When the method is implemented on a general-purpose processor, the conversion of signals between any sampling rates can be realized with very low complexity.

Description

Method for converting sampling rate of arbitrary multiple in software radio system

Technical Field

The invention relates to a method for converting sampling rate of arbitrary multiple in a software radio system, belonging to the technical field of wireless communication.

Background

In the traditional radio product development concept, both radio frequency and baseband processing are implemented by analog and digital circuits in a dedicated chip, and both signal parameters and processing are fixed. When new technologies emerge or versions need to be upgraded, new specialized chips must be developed to support them. In a software radio communication system, analog-digital and digital-analog conversion (AD/DA) are shifted to an antenna end as much as possible, and signal processing processes such as signal generation, modulation/demodulation, channel coding and decoding and protocol stacks are implemented by software, so that hardware circuit support is not needed. The software radio has reconfigurable characteristics, so that great flexibility is brought to product development and scientific research.

Different communication systems or air interface protocols have different transmission rates, corresponding to different symbol rates or master clock rates. This is obviously unacceptable if the main crystal is to be replaced each time the radio is reconfigured. In software radio systems, the sampling frequency of the AD/DA is therefore often fixed, and then the data of the required specific sampling rate is calculated by the software by means of digital sampling rate conversion. At the receiving end, the data is typically converted from the original sampling rate of the AD to an integer multiple of the symbol rate, and then demodulated. At the transmitting end, the data generated by digital modulation is often an integer multiple of the symbol rate, and the data is converted into the sampling rate of DA and sent to the radio frequency unit for processing and transmission.

Sample rate conversion can be accomplished if the new sample rate is an integer multiple or fraction of the AD/DA sample frequency, up-sampling (interpolation) and down-sampling (decimation) commonly used in digital signal processing. If the relationship between the new and old sample rates is a ratio of two simple integers, e.g., 3/5, the sample rate conversion can be achieved by a method of up-sampling by a factor of 3 and down-sampling by a factor of 5. However, if the ratio of the new and old sample rates is a complex rational number, such as 1.117, upsampling 1117 times followed by downsampling 1000 times is a very inefficient implementation. Further, if the ratio of the new and old sampling rates is irrational, e.gThe method of up-down sampling combination is not applicable at all.

For any multiple of the sample rate conversion problem, the current common approach is to resample using a time-varying low-pass filter of the Farrow structure. The coefficient of the reconstruction filter is calculated in real time according to each new sampling moment, and then convolution operation is carried out on the coefficient and the data under the old sampling rate, so as to obtain the interpolation data under the new sampling moment. To reduce the computational effort, the Farrow structure uses piecewise polynomial fitting to approximate the time domain response of the reconstruction filter and employs a nested computational approach to reduce the complexity of the exponentiation. Thus, when an nth order polynomial is used to fit the reconstruction filter, the resampling is calculated approximately N times that of a normal low pass filter.

For a sampling rate conversion system realized by a digital circuit, the Farrow structure is a good choice, and real-time calculation can be completed by parallel processing only by adding N times of multiplication and addition units, so that the processing time is not increased. However, for a software-implemented sample rate conversion system, all of the computations are done in the CPU or GPU, and an increase in the number of N times the computation results in an increase in the processing time by a factor of N.

The software wireless level platform based on the general processor adopts a commercial CPU/GPU server or a common personal computer as a signal processing platform, can adopt general high-level language (such as C/C++) to carry out software development, and has higher flexibility. Although the computing resources of general-purpose processors are limited, they generally have larger memory resources (computer memory or GPU memory), and the memory efficiency can be sacrificed to improve the computing efficiency, which is fundamentally different from the design concept of hardware processing.

Disclosure of Invention

In view of the above problems, the present invention provides a method for converting sampling rates at any multiple in a software radio system, which can implement real-time digital conversion between any two sampling rates of a signal.

The invention relates to a method for converting sampling rate of arbitrary multiple in a software radio system, which comprises a data preparation stage and a signal real-time processing stage, and specifically comprises the following steps:

the preparation phase comprises:

and establishing a first storage table for storing coefficients of the reconstruction filter corresponding to each new sampling moment.

And establishing a second storage table for storing old sampling moments corresponding to the input data of the reconstruction filter.

The signal real-time processing stage comprises the following steps:

segmenting an input data stream at an old sampling rate according to a period T; and for each new sampling moment in the signal period, reading the corresponding reconstruction filter coefficient and the corresponding old sampling moment according to the two storage tables, reading the input data at the old sampling rate, and calculating the output data at the new sampling rate.

The above processing is performed on all segments using two stored tables to obtain a resampled signal.

The invention has the advantages that:

1. the invention relates to a method for converting sampling rate of arbitrary multiple in a software radio system, which is characterized in that signals are processed in a segmentation way, the coefficient of a reconstruction filter required by each new sampling moment in a data block and the old sampling moment related to the filter input are calculated in advance according to the length of the segmented data block, the coefficients and the old sampling moment are stored, and the two data blocks are repeatedly used for filtering operation in the follow-up data block. Because the filter coefficients are known, the computational complexity of the time-varying coefficient resampling filter is equivalent to that of a common time-invariant low-pass filter, and only 1/N of the resampling filter with the Farrow structure is adopted. While the increased storage space is fully affordable to modern computers.

2. The method for converting the sampling rate of any multiple in the software radio system can realize the conversion from one sampling rate to any other sampling rate with low complexity, thereby meeting the requirement of real-time processing in the software radio system.

Drawings

FIG. 1 is a flow chart of a method of arbitrary multiple sample rate conversion in a software defined radio system in accordance with the present invention;

FIG. 2 is a comparison of filter coefficients for a rectangular window cut versus a Blackman window cut in an embodiment of the present invention;

FIG. 3 is a waveform and spectrum of signals before and after downsampling in accordance with an embodiment of the present invention;

FIG. 4 is a waveform and spectrum of signals before and after upsampling in an embodiment of the present invention;

FIG. 5 is a graph showing the resampling effect after reducing the number of filter truncations in an embodiment of the invention;

FIG. 6 is a resampling effect after increasing the filter truncation count in an embodiment of the invention;

FIG. 7 is a graph showing the resampling effect of a Blackman window applied to a filter impulse response in an embodiment of the invention;

fig. 8 shows an irrational multiple sample rate conversion effect in an embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION

The invention is described in further detail below with reference to the accompanying drawings.

For a digital signal, one wants to use from a sampling rate f _s Converted to another sampling rate f _s ' the digital signal may be first sampled at a rate f _s The DA of (1) obtains an analog signal and then goes through a sampling rate f _s The' AD gets a new digital signal. However, this operation is complicated to implement because of the involvement of the hardware AD/DA (and the clock control behind, etc.). Sample rate conversion is typically performed in software radio systems using purely digital processing methods.

The idea of using pure digital processing for sample rate conversion is also to reconstruct a digital signal at one sample rate into an analog signal and then sample the reconstructed analog signal at another sample rate. However, it is found that the two-step operation is combined to directly calculate the digital signal at the new sampling rate by passing the digital signal at the old sampling rate through a digital reconstruction filter of a time-varying coefficient without actually converting the digital signal to an analog signal.

Assume an old sampling rate f _s ＝1/T _s The lower discrete time digital signal is x n]Using the following impulse train signal x _s (t) to recover the continuous-time signal,

wherein T is _s Is the old sampling period; n is a discrete time digital signal x [ n ]]Is only an integer; t is a continuous time; delta (·) is the impulse function.

The reconstruction filter is a continuous time ideal low-pass filter, and the impulse response is

Wherein Ω _c The bandwidth of the reconstruction filter, here taken as Ω _c ＝π/T _s . The reconstructed continuous time signal is:

wherein, the symbol "×" represents convolution operation, sa (·) is a sampling function;

from the above derivation, x is reconstructed by interpolation of the Sa function _c After (t), for x again _c (t) at a new sampling rateSampling, namely:

wherein y [ m ]]Is reconstructed data at a new sampling rate; m is the index of the new sample rate data; t (T) _s ' is the new sampling period; r is the sample rate conversion factor and,

from the above, it can be derived that the discrete-time reconstruction filter is an infinitely long time-varying coefficient filter, expressed as

At each new sampling instant mT _s ' a set of filter coefficients h [ m, n are all recalculated]. Because an infinitely long time-varying coefficient cannot be constructed in practical application, the time-varying coefficient can be truncated by using a window function, and a new sampling point can be calculated by using a finite-length filter coefficient. Given ginsengThe number L (set according to the requirement of the calculated amount) is that the filter length is 2L+1, and only 2L+1 filter coefficients are calculated at each new sampling moment, namely

Wherein w (·) represents a window function, a symbolRepresenting a rounding down.

Given the parameter L, the filter coefficient depends on the inter-sample position as known from the expression and the variable value range

Thus there is

When r is a rational number, mu _m The filter coefficient can be repeatedly utilized in each period along with the periodical change of m; when r is irrational number, mu _m The filter coefficients vary irregularly with m, at different points m.

If h [ m, n ] is calculated in real time using the above formula, the calculation amount is very large because trigonometric functions and division operations are included. Thus Farrow in paper "c.w.farrow," A continuously variable digital delay element, "in proc.ieee International Symposium on Circuits and Systems, espoo, finland, june 6-9,1988, pp.2641-2645," proposes a method for calculating h [ m, n ] using piecewise polynomial fitting. The polynomial coefficients are invariant given the filter impulse response to be fitted, and this approach requires only some multiplication to recalculate the coefficients of the filter as the time difference (mr-n) varies.

The general form of the Farrow filter can be represented by the following formula

Wherein N-1 is the polynomial order, M is the polynomial segmentation number, c _i (. Cndot.) is a polynomial coefficient. The above formula can be further simplified as:

wherein the method comprises the steps of

In particular, it is usually calculated according to the above formulaThen adopting nested structure to calculate y m]To reduce the number of multiplication operations. Taking n=3 as an example, there are

It can be seen that in the Farrow filter the polynomial segmentation number M corresponds to the length 2l+1 of the time-varying reconstruction filter mentioned above. For the N-1 order polynomial fit, the total computation of the Farrow filter is approximately N (2L+1). The higher the order of the polynomial fit, the closer the Farrow filter is to the ideal reconstruction filter, but the more computationally intensive it will be.

In software defined radio systems, the computation is performed in a CPU or GPU, and thus an increase in the amount of computation results in an increase in processing time. In contrast, general-purpose processing platforms typically possess rich memory resources that can be sacrificed in memory efficiency to increase computational efficiency. Therefore, in the method for converting sampling rate of arbitrary multiple in the software radio system, the signals are segmented, the coefficients of the reconstruction filter required by each new sampling time in the data block and the old sampling time related to the filter input are calculated in advance according to the length of the segmented data block, the coefficients and the old sampling time related to the filter input are stored, and the two groups are repeatedly used for filtering operation in all the subsequent data blocks, as shown in fig. 1, the specific design steps are as follows:

step 1: data preparation.

Knowing the old sampling rate f _s And a new sampling rate f _s ' calculating a sampling rate conversion factor r=f _s /f _s 'A'; determining a period T of the signal segment; the truncated length 2l+1 of the reconstruction filter, and the window function w (n) used for the truncation. The signal segment period T should be generally greater than 1000 times the symbol period to reduce the discontinuity between the signal segments; the puncturing length 2l+1 should be generally 3 or more to reduce signal distortion caused by puncturing effect.

Step 2: and calculating and storing coefficients of the reconstruction filter corresponding to each new sampling moment as a storage table I.

Segmenting the signal with T as a period, and sharing P=T/T at the old sampling rate _s With a new sampling rate, P' =t/T is shared by the sampling points _s ' sample points. For each new sampling instant mT _s ' 2L+1 filter coefficients are calculated and stored

Will be described above as h [ m, n ]]The index n of (1) is replaced with L, l=0, 1,2,3, 2L; and then translate to the leftAnd (3) a plurality of points, obtaining:

the filter length 2l+1 can be intuitively embodied.

Thus P' (2l+1) filter coefficients are stored in total as a stored table one.

Step 3: the old sampling time corresponding to the filter input data (old sampling rate data) is stored as a second storage table.

For each new sampling instant mT _s ' storing old sampling time corresponding to the input data of the reconstruction filter:

where the index m of the new sample rate data is an integer having a value of 1,2,3,4 … P'.

In this way, P' old sampling moments are stored as a second memory table.

Step 4: and carrying out real-time processing on the subsequent signals according to the first storage table and the second storage table obtained in the previous steps.

(1) The input data at the old sampling rate is segmented according to a period T, each segment being a signal block.

(2) And for each new sampling time in the signal period, reading the corresponding filter coefficient and the corresponding old sampling time according to the two storage tables.

(3) The segmented data at the old sampling rate is read and the output data at the new sampling rate is calculated. For each new sampling time m, the old sampling time t [ m ] is corresponding, 2L+1 data are found in the input data under the old sampling rate, and 2L+1 data start from x [ t [ m ] to x [ t [ m ] +2L ] end; multiplying and then accumulating the data with the filter coefficient h'm, l to obtain y m, namely:

(4) And (3) processing all the segmented data in the steps (2) and (3) to obtain a resampled signal.

It can be seen that since the filter coefficients are known, only 2l+1 multiplications are required for each new sample point, the computational complexity of such a time-varying coefficient resampling filter is comparable to that of a normal, non-lowpass filter, only 1/N of the Farrow structure resampling filter.

Since the new sampling instants of each data block start from zero, there may be some discontinuities between the data blocks, the starting instants of the signal blocks being at most offset T compared to a continuous processing without blocking _s '. In the case of oversampling, the effect of such a discontinuity is small. The inherent clock bias between transceivers in a wireless communication system, the relative movement of the transceivers may also cause the symbol period to scale, both of which may have a greater impact than the impact of discontinuities between data blocks. During demodulation, a time-offset tracking loop is typically used to correct for such synchronization bias. Of course, the length of the data blocks can be increased as much as the memory space permits to reduce such discontinuities, and then the effect of such inter-block discontinuities is substantially negligible after time-offset tracking and compensation.

Examples:

the effect of the implementation of the method according to the invention is illustrated below. Considering that a signal transmission system is built by using a certain software radio platform, the basic flow of the received signal processing mainly comprises down-conversion, low-pass filtering, resampling, demodulation and the like.

In the preparation phase, firstly, the receiver parameters are configured, the signal segment length is set to be 100ms, and the initial sampling rate f is determined _s And a new sampling rate f _s ' the conversion factor r is calculated. Thereafter, the reconstruction filter truncation length 2l+1 and the window function w (n) are determined. Finally, all ofStored as a sampling schedule, while being dependent on μ _m And calculating 2L+1 filter coefficients corresponding to each moment, and storing the 2L+1 filter coefficients into a reconstructed filter coefficient table. Fig. 2 gives l=10, μ _m =0.25, using rectangular window and Blackman window truncated reconstructed filter coefficients, respectively. If f _s ＝10MHz，f _s ' 3.2MHz, using 32 bit integer stored sample times, using 32 bit single precision floating point number storage to reconstruct the filter coefficients, the schedule and coefficient table would occupy approximately 1.28MB and 26.88MB of storage space, respectively.

In the real-time processing stage, the signal is segmented and the baseband signal is obtained by down-conversion. And repeatedly using two storage tables, and carrying out reconstruction filtering on each section of original signal to obtain a resampled signal.

Fig. 3 shows waveforms and spectra before and after resampling when a BPSK signal is received. BPSK symbol rate is 400KHz, single-side bandwidth of low-pass filter is set to 400KHz, initial sampling rate f _s =10 MHz. In this case, 25 samples are included in one symbol, but in fact we do not need to have such a high oversampling rate, considering downsampling to f for the convenience of subsequent real-time processing _s ' 3=2 MHz, the reconstruction filter is truncated using a rectangular window, l=10. Resampling produces image components on the spectrum, while spectral leakage due to time domain truncation can impair the stopband attenuation capability of the reconstruction filter. Although the suppression of the image component is insufficient here, there is also about 40dB of attenuation with respect to the main lobe. As can be seen from the time domain waveform, the resampled signal is not significantly distorted, and the presence of the image component does not affect the subsequent demodulation and other processes.

Fig. 4 shows waveforms and spectra before and after resampling when receiving an LTE signal. The highest sampling rate of the receiver can only reach 20MHz, limited by the platform hardware. For facilitating subsequent processing, the signal needs to be received with a 20MHz sampling rate, then up-sampled to 30.72MHz, the reconstruction filter is truncated using a rectangular window, l=10. Since the bandwidth of LTE signals is larger (about 18 MHz), the effects of mirror aliasing are also more severe. However, the distortion degree is found to be low by comparing the signal waveforms before and after resampling, and the subsequent processing is not affected.

For rational multiples of sample rate conversion, one common approach is interpolation-low pass filtering-decimation. Consider f _s ＝10MHz，f _s ' 3.2MHz, 8-fold interpolation and 25-fold decimation are required, and on a computer using Intel Core i7-11800H central processing unit, the average processing time per block of data is 32ms. On the same computer, the average processing time of the invention is only 4.5ms, and the real-time performance is better. In addition, if the Farrow reconstruction filter of the 4 th order polynomial is considered, its run time is about 5 times that of the present invention.

For the above case of receiving BPSK signals, l=5 and l=20 are taken, respectively, and the resampling results are shown in fig. 5 and 6. It can be seen that by increasing the truncated length of the reconstruction filter, the rejection of the image component can be enhanced.

If there are more stringent requirements for image rejection, it is contemplated to truncate the reconstruction filter using a smoothly transitioned window function. FIG. 7 shows that at f _s ＝10MHz，f _s In the case of' =3.2mhz, l=10, the reconstruction filter is truncated by using the Blackman window, and the pre-and post-sampling signal waveforms and spectra are resampled. The image component is now almost completely suppressed and the image attenuation is greater than 50dB.

For irrational multiples of the sample rate transform, the distribution of the image components is irregular and will necessarily alias onto the main spectrum lobe, so it is also necessary to adequately suppress the image by windowing. FIG. 8 shows the resampling results for the case of irrational multiple sample rate conversion of the present invention, where f _s ＝10MHz，L=10, the window function uses a Blackman window. It can be seen that the method of the invention still has good effect on sampling rate conversion of irrational multiples.

Claims (6)

1. A method of arbitrary multiple sample rate conversion in a software defined radio system, characterized by: the method comprises a preparation stage and a signal real-time processing stage;

the preparation phase comprises:

establishing a first storage table for storing coefficients of a reconstruction filter corresponding to each new sampling moment;

establishing a second storage table for storing old sampling moments corresponding to the input data of the reconstruction filter;

the signal real-time processing stage comprises the following steps:

segmenting an input data stream at an old sampling rate according to a period T; for each new sampling moment in the signal period, reading the corresponding reconstruction filter coefficient and the corresponding old sampling moment according to the two storage tables, reading the input data at the old sampling rate, and calculating the output data at the new sampling rate;

the above process is performed on all segments using two memory tables.

2. A method of arbitrary multiple sample rate conversion in a software defined radio system as defined in claim 1 wherein: the method for establishing the first storage table comprises the following steps:

with T as period for input signal x [ n ]]Segmentation is performed, and P=T/T is shared under the old sampling rate _s With a new sampling rate, P' =t/T is shared by the sampling points _s ' sample points; for each new sampling instant mT _s ' 2L+1 filter coefficients are calculated and stored

Wherein m is an index of new sampling rate data, and m is an integer with values of 1,2,3,4 and … P'; t (T) _s Is the old sampling period; t (T) _s ' is the new sampling period; r is the sample rate conversion factor and,n is the signal x [ n ]]Index of (2); w (·) represents the window function, signRepresenting a downward rounding; l is a parameter set according to the calculation amount requirement, and 2L+1 is the filter length;

will be described above as h [ m, n ]]The index n in (a) is replaced by l, and the left shift is performed againAnd (3) a plurality of points, obtaining:

p' (2l+1) filter coefficients are stored in total as a first storage table.

3. A method of arbitrary multiple sample rate conversion in a software defined radio system as defined in claim 1 wherein: the method for establishing the second storage table comprises the following steps:

for each new sampling instant, the old sampling instant corresponding to the reconstruction filter input data is stored:

wherein m is an index of new sampling rate data, and m is an integer with values of 1,2,3,4 and … P'; p' is the number of sampling points at the new sampling rate; r is a sampling rate conversion factor; l is a parameter set according to the calculation amount requirement, and 2L+1 is the filter length;

p' old sampling instants are stored altogether as a second memory table.

4. A method of arbitrary multiple sample rate conversion in a software defined radio system as defined in claim 1 wherein: the output data calculation method under the new sampling rate comprises the following steps:

for each new sampling time m, the old sampling time t [ m ] is corresponding, 2L+1 data are found in the input data under the old sampling rate, and 2L+1 data start from x [ t [ m ] to x [ t [ m ] +2L ] end; multiplying and then accumulating the data with h'm, l to obtain y m, namely:

。

5. a method of arbitrary multiple sample rate conversion in a software defined radio system as defined in claim 1 wherein: t is greater than 1000 times the symbol period.

6. A method of arbitrary multiple sample rate conversion in a software defined radio system as defined in claim 1 wherein: 2L+1 is 3 or more.