CN112422103B - Method for reducing number of raised cosine filter multipliers and FIR raised cosine filter - Google Patents

Method for reducing number of raised cosine filter multipliers and FIR raised cosine filter Download PDF

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CN112422103B
CN112422103B CN202011341582.1A CN202011341582A CN112422103B CN 112422103 B CN112422103 B CN 112422103B CN 202011341582 A CN202011341582 A CN 202011341582A CN 112422103 B CN112422103 B CN 112422103B
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filter
raised cosine
transfer function
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常凯
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Shanghai Qingkun Information Technology Co Ltd
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0202—Two or more dimensional filters; Filters for complex signals
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0211—Frequency selective networks using specific transformation algorithms, e.g. WALSH functions, Fermat transforms, Mersenne transforms, polynomial transforms, Hilbert transforms
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0223—Computation saving measures; Accelerating measures
    • H03H17/0225—Measures concerning the multipliers
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0223—Computation saving measures; Accelerating measures
    • H03H17/0227—Measures concerning the coefficients
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0248—Filters characterised by a particular frequency response or filtering method
    • H03H17/028—Polynomial filters
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H2017/0072—Theoretical filter design
    • H03H2017/0081—Theoretical filter design of FIR filters

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Abstract

The invention provides a method for reducing the number of multipliers of a raised cosine filter and the FIR raised cosine filter, wherein the method comprises the following steps: designing a traditional FIR raised cosine filter according to the application requirement of the raised cosine filter, and determining transfer function polynomial coefficients of the traditional FIR raised cosine filter; decomposing the traditional FIR raised cosine filter into a pre-filter and an equalization filter; and modifying transfer function polynomial coefficients of the traditional FIR raised cosine filter to ensure that the transfer function of the optimized system is zero at w=pi, and factoring factors of the zero points to obtain transfer function polynomials corresponding to the pre-filter and the equalization filter. The optimized FIR raised cosine filter can reduce the number of multipliers on the premise of ensuring unchanged performance, thereby being convenient for the use of the FIR raised cosine filter.

Description

Method for reducing number of raised cosine filter multipliers and FIR raised cosine filter
Technical Field
The present invention relates to the field of wireless communications technologies, and in particular, to a method for reducing the number of multipliers of a raised cosine filter and a FIR raised cosine filter.
Background
The raised cosine filter (Raised cosine filter, RCF) is a pulse shaping filter for broadband data communications. The Impulse Response (IR) of the RCF is zero at the alternation of adjacent symbols, so that the RCF can effectively suppress inter-symbol interference (Inter Symbol Interference, ISI) of the transmitted data, and the digital RCF is typically physically implemented in the form of a finite Impulse Response (Finite Impulse Response, FIR) or infinite Impulse Response (Infinite Impulse Response, IIR) filter. The FIR raised cosine filter has linear phase, stable operation and is more commonly used in practice.
The filter of the direct structure FIR consists of delay elements, adders and multipliers, and the number of multipliers required for realizing the FIR raised cosine filter is in linear relation with the length of the filter L. For example, a type I symmetric RCF of L (L is an odd number) length requires (L-1)/2+1 multipliers.
However, as the multiplier has more gates on the underlying structure, the filter with the multi-multiplier structure is often larger in scale, higher in complexity and higher in power consumption, and the use of the filter in the fields of limited power consumption, such as satellite communication, is affected. Therefore, there is a need for an FIR raised cosine filter that can reduce the number of multipliers while ensuring constant performance.
Disclosure of Invention
The invention aims to provide a method for reducing the number of multipliers of a raised cosine filter and the FIR raised cosine filter, which can reduce the number of the multipliers on the premise of ensuring the unchanged performance, thereby being convenient for the use of the FIR raised cosine filter.
The technical scheme provided by the invention is as follows:
the invention provides a method for reducing the number of raised cosine filter multipliers, which comprises the following steps:
Designing a traditional FIR raised cosine filter according to the application requirement of the raised cosine filter, and determining transfer function polynomial coefficients of the traditional FIR raised cosine filter;
decomposing the traditional FIR raised cosine filter into a pre-filter and an equalization filter;
and modifying transfer function polynomial coefficients of the traditional FIR raised cosine filter to ensure that the transfer function of the optimized system is zero at w=pi, and factoring factors of the zero points to obtain transfer function polynomials corresponding to the pre-filter and the equalization filter.
According to the scheme, the traditional FIR raised cosine filter is decomposed into the front filter and the equalization filter, the polynomial coefficient of the transfer function of the traditional FIR raised cosine filter is modified, the transfer function of the optimized system is zero at w=pi, the factor of the zero point is factorized, the transfer function polynomial corresponding to the front filter and the equalization filter can be obtained, the optimized FIR raised cosine filter is further obtained, the number of multipliers of the equalization filter can be reduced through the optimization, the number of multipliers of the whole FIR raised cosine filter is reduced, and the use of the FIR raised cosine filter in occasions such as limited power consumption is facilitated.
Further, the determining the transfer function polynomial coefficient of the conventional FIR raised cosine filter specifically includes:
the transfer function H (z) of the traditional N-order FIR raised cosine filter is determined as follows:
Wherein n=4k+2 or 4k, k is an integer, and h 0'、h1、h2…hN/2 is a polynomial coefficient of a transfer function of the conventional N-order FIR raised cosine filter;
and determining the specific transfer function polynomial coefficient of the traditional FIR raised cosine filter according to the specific order of the traditional FIR raised cosine filter to be designed.
Further, modifying the transfer function polynomial coefficient of the conventional FIR raised cosine filter to make the transfer function of the optimized system be zero at w=pi, factoring the factor of zero to obtain transfer function polynomials corresponding to the pre-filter and the equalization filter, which specifically includes:
Modifying a polynomial coefficient h 0' of a transfer function of the traditional N-order FIR raised cosine filter to be 2 (h 1-h2+h3-h4 + …);
And (3) enabling the transfer function of the optimized system to be zero at w=pi, extracting a factorization structure, and obtaining transfer function polynomials corresponding to the pre-filter and the equalization filter:
Wherein b 0、b1、b2…hN/2-1 is the polynomial coefficient of the transfer function of the equalization filter, an
Transfer function H (z) = (1+z -1)2) of the pre-filter.
Further, the conventional FIR raised cosine filter has a zero at z= -1.
Further, the pre-filter selects a (1+z -1) type filter.
Further, the equalization filter is a finite impulse response filter.
Further, the pre-filter and the equalization filter are connected in a cascade connection.
Further, after the transfer function polynomials corresponding to the pre-filter and the equalization filter are obtained, the method further includes the steps of:
And calculating the intersymbol interference suppression capability of the optimized FIR raised cosine filter, and comparing the intersymbol interference suppression capability with the intersymbol interference suppression capability of the traditional FIR raised cosine filter.
Further, after the transfer function polynomials corresponding to the pre-filter and the equalization filter are obtained, the method further includes the steps of:
And calculating the optimized filter coefficient sensitivity of the FIR raised cosine filter, and comparing the filter coefficient sensitivity with the filter coefficient sensitivity of the traditional FIR raised cosine filter.
In addition, the invention also provides an FIR raised cosine filter which is obtained by the method for reducing the number of the multipliers of the raised cosine filter.
According to the method for reducing the number of the multipliers of the raised cosine filter and the FIR raised cosine filter, the traditional FIR raised cosine filter is decomposed into the front filter and the equalization filter, the polynomial coefficient of the transfer function of the traditional FIR raised cosine filter is modified, the transfer function of an optimized system is zero at w=pi, the factors of the zero are decomposed in a factorization mode, transfer function polynomials corresponding to the front filter and the equalization filter can be obtained, the optimized FIR raised cosine filter is further obtained, the number of the multipliers of the equalization filter can be reduced through the optimization, the number of the multipliers of the whole FIR raised cosine filter is reduced, and the use of the FIR raised cosine filter in occasions such as limited power consumption is facilitated.
Drawings
The above features, technical features, advantages and implementation modes of the present invention will be further described in the following description of preferred embodiments with reference to the accompanying drawings in a clear and understandable manner.
FIG. 1 is a schematic overall flow diagram of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a conventional 10-order FIR raised cosine filter according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the structure of an optimized 10-order FIR raised cosine filter according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the coefficient sensitivity curves of a conventional FIR raised cosine filter and an optimized FIR raised cosine filter according to an embodiment of the present invention;
FIG. 5 is a graph showing the amplitude-frequency response of different quantized bits according to an embodiment of the invention;
FIG. 6 is a schematic diagram of an impulse response of an FIR raised cosine filter according to an embodiment of the present invention;
fig. 7 is a schematic diagram of an amplitude-frequency response of an FIR raised cosine filter according to an embodiment of the present invention.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will explain the specific embodiments of the present invention with reference to the accompanying drawings. It is evident that the drawings in the following description are only examples of the invention, from which other drawings and other embodiments can be obtained by a person skilled in the art without inventive effort.
For the sake of simplicity of the drawing, the parts relevant to the present invention are shown only schematically in the figures, which do not represent the actual structure thereof as a product. Additionally, in order to simplify the drawing for ease of understanding, components having the same structure or function in some of the drawings are shown schematically with only one of them, or only one of them is labeled. Herein, "a" means not only "only this one" but also "more than one" case.
Example 1
In one embodiment of the present invention, as shown in fig. 1, the present invention provides a method for reducing the number of multipliers of a raised cosine filter, comprising the steps of:
S1, designing a traditional FIR raised cosine filter according to application requirements of the raised cosine filter, and determining transfer function polynomial coefficients of the traditional FIR raised cosine filter.
Preferably, the polynomial of the conventional FIR raised cosine filter in this scheme needs to have a zero at z= -1.
Preferably, determining transfer function polynomial coefficients of a conventional FIR raised cosine filter specifically includes:
The transfer function H (z) of the conventional N-order FIR raised cosine filter is determined as:
Wherein n=4k+2 or 4k, k is an integer, h 0'、h1、h2…hN/2 is a polynomial coefficient of a transfer function of a conventional N-order FIR raised cosine filter; the specific transfer function of the FIR raised cosine filter is determined according to the specific order of the conventional FIR raised cosine filter to be designed.
S2, decomposing the traditional FIR raised cosine filter into a pre-filter and an equalization filter.
Preferably, in the present solution, the equalization filter is a finite impulse response filter.
Further preferably, the pre-filter and the equalization filter are connected in a cascade connection.
S3, modifying transfer function polynomial coefficients of a traditional FIR raised cosine filter, enabling the transfer function of the optimized system to be zero at the position of w=pi, factoring factors of the zero, and obtaining transfer function polynomials corresponding to the pre-filter and the equalization filter.
The method specifically comprises the following steps: modifying a polynomial coefficient h 0' of a transfer function of a traditional N-order FIR raised cosine filter to be 2 (h 1-h2+h3-h4 + …); and (3) enabling the transfer function of the optimized system to be zero at the position of w=pi, extracting a factorization structure, and obtaining transfer function polynomials corresponding to the pre-filter and the equalization filter:
wherein b 0、b1、b2…hN/2-1 is the polynomial coefficient of the transfer function of the modified equalization filter, an
Transfer function H (z) = (1+z -1)2) of the pre-filter.
Further preferably, the pre-filter selects a (1+z -1) type filter.
According to the scheme, the traditional FIR raised cosine filter is decomposed into the front filter and the equalization filter, the polynomial coefficient of the transfer function of the traditional FIR raised cosine filter is modified, the transfer function of the optimized system is zero at w=pi, the factor of the zero point is factorized, the transfer function polynomial corresponding to the front filter and the equalization filter can be obtained, the optimized FIR raised cosine filter is further obtained, the number of multipliers of the equalization filter can be reduced through the optimization, the number of multipliers of the whole FIR raised cosine filter is reduced, and the use of the FIR raised cosine filter in occasions such as limited power consumption is facilitated.
Example 2
In one embodiment of the present invention, based on embodiment 1, the FIR raised cosine filter to be designed in this embodiment is a10 th order FIR raised cosine filter, and a schematic structure diagram of a conventional 10 th order FIR raised cosine filter is shown in fig. 2, where a transfer function H (z) of the conventional 10 th order FIR raised cosine filter is:
Changing the coefficient h 0' into h 0'＝2(h1-h2+h3-h4+h5), and after transformation:
Wherein,
The transfer functions of the pre-filter and the equalization filter can be obtained, and then the optimized 10-order FIR raised cosine filter is obtained, and the structure diagram of the optimized 10-order FIR raised cosine filter is shown in fig. 3, so that one multiplier is omitted compared with the original 10-order FIR raised cosine filter. In other embodiments, FIR raised cosine filters of other orders may also be obtained according to the method.
Example 3
In one embodiment of the present invention, after obtaining the transfer function polynomials corresponding to the pre-filter and the equalization filter on the basis of embodiment 1 or 2, the method further comprises the steps of:
and calculating the intersymbol interference suppression capability of the optimized FIR raised cosine filter, and comparing the intersymbol interference suppression capability with the intersymbol interference suppression capability of the traditional FIR raised cosine filter.
In digital communication systems, pulses may arrive at different time intervals due to non-constant group delay as they are transmitted through dispersive channels. Thus, intersymbol interference (Inter Symbol Interference, ISI) may occur.
To deal with ISI, the Nyquist criterion, i.e. the sample value distortion-free criterion, is first met, i.e. when the pulse p (t) is transmitted over a bandwidth-limited channel, the original signal code can still be recovered without errors during resampling as long as the sample value at a specific point remains unchanged even if the entire received waveform is changed, and at this time the pulse has enough bandwidth to allow the full spectrum of the transmitted signal to pass. The sample value distortion-free criterion is as follows:
Where T b is the pulse sampling time. This means that the system impulse response is only one non-zero sample at the sampling instant. As summary of the invention, we modify h 0' to 2 (h 1-h2+h3-h4 + …) to achieve zero at z= -1. After modification, the impulse frequency response still has only one non-zero sampling value, namely h 0', so that the scheme can effectively inhibit ISI; on the other hand, the stop band attenuation is about 5db, and no obvious adverse effect is brought to the system performance.
Further, after obtaining transfer function polynomials corresponding to the pre-filter and the equalization filter, the method further comprises the steps of:
And calculating the filter coefficient sensitivity of the optimized FIR raised cosine filter, and comparing the filter coefficient sensitivity with the filter coefficient sensitivity of the traditional FIR raised cosine filter.
The filter coefficient sensitivity is used to represent the sensitivity of a given coefficient in the system to the change in the overall transfer function caused by the change. For comparison purposes, we only choose to compare coefficients h 0'、h1、h2 and h 3 of the conventional filter structure, coefficients b 0、b1、b2 and b 3 of the inventive structure of this scheme.
Fig. 4 depicts the coefficient sensitivity curves of a conventional FIR raised cosine filter and an optimized FIR raised cosine filter. As can be seen from the figure, the sensitivity of the conventional structure filter at zero point is very high, h 0' is about 80, h 1 is 75, h 2 is 50, h 3 is 20, the sensitivity of the filter of the structure of the invention is obviously reduced, b 0 is 5, b 1 is 3, b 2 is 10, b 3 is 2, and the average sensitivity of the filter coefficient is reduced by about 90%.
Another method of checking the sensitivity of the coefficients is quantization error. Fig. 5 shows a schematic diagram of an Amplitude-frequency response (AR) with different quantization bits (i.e. different quantization errors). The FIR coefficients of the inventive structure are quantized to 16/14/12/10/8 bits and 10/12/14/16 bits respectively, and still have a stop band attenuation of-45 db, which is sufficient to filter noise in a channel. Therefore, the structure of the invention can effectively reduce the coefficient bit number requirement of the filter, and meanwhile, the structure only has 20 coefficients, and compared with the structure, the hardware implementation cost of the invention is reduced by [1- (20/21) × (10/16) ] ×100% ≡40%.
Example 4
In one embodiment of the present invention, the present invention further provides an FIR raised cosine filter, which is obtained by the method for reducing the number of multipliers of the raised cosine filter in any one of the above embodiments.
Specifically, in this embodiment, we modeled a satellite communication link system and tested the performance of the inventive FIR raised cosine filter structure through this link system. In this model, the random source information symbol rate is 1×10 6 symbols/sec, and Quadrature phase shift keying (Quadrature PHASE SHIFT KEYING, QPSK) modulation is used; the modulated complex signal is FIR-shaped filtered and then transmitted through an Additive White Gaussian Noise (AWGN) channel with a signal-to-Noise ratio of 10dB (3 dB above the QPSK threshold). In the simulated scenario, the satellite orbit height H is set to 600 km, the satellite velocity at this orbit height is about 7.56 km/s, the rf frequency f of the transmitted signal is 500 mhz, and the apparent satellite pitch angle is about 24 degrees on the ground, at which time the doppler shift is about 10kHz.
In this embodiment, a square root FIR is designed. Since the theoretical FIR has an impulse response of infinite length, we truncate the impulse response to 10 symbols of 4 samples each. The filter length L is 41. The filter order N is 40 and the roll-off coefficient α is set to 0.35. The impulse response IR and amplitude-frequency response AR of the FIR raised cosine filter are shown in fig. 6 and fig. 7, respectively.
In this embodiment, the simulation time is 200ms. In the simulation, 1×10 6 bits of information are transmitted in total, wherein the error number is 8. After one hundred trials, the average bit error rate was calculated to be approximately 1×10 -5. In addition, as shown in the following table, the optimized FIR raised cosine filter of the scheme has the same performance as the conventional FIR raised cosine filter.
It should be noted that the above embodiments can be freely combined as needed. The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.

Claims (8)

1. A method for reducing the number of raised cosine filter multipliers, comprising the steps of:
Designing a traditional FIR raised cosine filter according to the application requirement of the raised cosine filter, and determining transfer function polynomial coefficients of the traditional FIR raised cosine filter;
decomposing the traditional FIR raised cosine filter into a pre-filter and an equalization filter;
Modifying transfer function polynomial coefficients of a traditional FIR raised cosine filter to enable the transfer function of the optimized system to be zero at w=pi, factoring factors of the zero to obtain transfer function polynomials corresponding to the pre-filter and the equalization filter;
the determining the transfer function polynomial coefficient of the traditional FIR raised cosine filter specifically comprises:
the transfer function H (z) of the traditional N-order FIR raised cosine filter is determined as follows:
Wherein n=4k+2 or 4k, k is an integer, and h 0'、h1、h2…hN/2 is a polynomial coefficient of a transfer function of the conventional N-order FIR raised cosine filter;
determining specific transfer function polynomial coefficients of the traditional FIR raised cosine filter according to specific orders of the traditional FIR raised cosine filter to be designed;
Modifying transfer function polynomial coefficients of the traditional FIR raised cosine filter to make the transfer function of the optimized system be zero at w=pi, factoring factors of zero points to obtain transfer function polynomials corresponding to the pre-filter and the equalization filter, specifically including:
Modifying a polynomial coefficient h 0' of a transfer function of the traditional N-order FIR raised cosine filter to be 2 (h 1-h2+h3-h4 + …);
And (3) enabling the transfer function of the optimized system to be zero at w=pi, extracting a factorization structure, and obtaining transfer function polynomials corresponding to the pre-filter and the equalization filter:
wherein b 0、b1、b2…bN/2-1 is the polynomial coefficient of the transfer function of the equalization filter, an
Transfer function H (z) = (1+z -1)2) of the pre-filter.
2. The method of reducing the number of raised cosine filter multipliers of claim 1, wherein: the conventional FIR raised cosine filter has a zero at z= -1.
3. The method of reducing the number of raised cosine filter multipliers of claim 1, wherein: the pre-filter selects a (1+z -1) type filter.
4. The method of reducing the number of raised cosine filter multipliers of claim 1, wherein: the equalization filter is a finite impulse response filter.
5. The method of reducing the number of raised cosine filter multipliers of claim 1, wherein: the pre-filter and the equalization filter are connected in a cascade connection mode.
6. The method for reducing the number of multipliers of a raised cosine filter according to claim 1, wherein after obtaining transfer function polynomials corresponding to the pre-filter and the equalization filter, the method further comprises the steps of:
And calculating the intersymbol interference suppression capability of the optimized FIR raised cosine filter, and comparing the intersymbol interference suppression capability with the intersymbol interference suppression capability of the traditional FIR raised cosine filter.
7. The method for reducing the number of multipliers of a raised cosine filter according to claim 1, wherein after obtaining transfer function polynomials corresponding to the pre-filter and the equalization filter, the method further comprises the steps of:
And calculating the optimized filter coefficient sensitivity of the FIR raised cosine filter, and comparing the filter coefficient sensitivity with the filter coefficient sensitivity of the traditional FIR raised cosine filter.
8. A FIR raised cosine filter obtained by the method of reducing the number of raised cosine filter multipliers as claimed in any of claims 1-7.
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CN108880506A (en) * 2018-06-07 2018-11-23 西安电子科技大学 A kind of implementation method of fitting of a polynomial digital filter
CN110705037A (en) * 2019-09-10 2020-01-17 深圳市南方硅谷半导体有限公司 Method, device, equipment and storage medium for optimizing FIR filter
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