CN104135457A - Digital phase discrimination method and device based on improved CORDIC (coordinated rotation digital computer) algorithm - Google Patents

Abstract

The invention discloses a digital phase discrimination method and device based on improved CORDIC (coordinated rotation digital computer) algorithm. The method comprises the following steps: firstly performing analog-to-digital conversion on an analog input signal to obtain a corresponding sampling digital signal; secondly, performing digital down conversion on the sampling digital signal to obtain a base band video I/Q signal; and finally, using the base band video I/Q signal in the step (2) as initial data of the improved CORDIC algorithm, performing iterative operation until the iterative result meets the accuracy requirement, and extracting phase information of the analog input signal from the iterative result. The problems that the phase discrimination result has great error and the phase discrimination accuracy is low under the condition that the module value of an input orthogonal signal is small are solved.

Description

Digital phase detecting method based on improved cordic algorithm and device

Technical field

The invention belongs to digital processing field, particularly digital phase detecting method and the device based on improved cordic algorithm.

Background technology

In traditional analogue phase detection circuit, because the frequency characteristic of analogue device generally can change along with the change of the environmental factors such as temperature, and when in circuit, analogue device is more, the accuracy of phase demodulation and the reliability of circuit working all can not be guaranteed.Along with the development of digital sample technology and being widely used of digital processing device, digital signal after sampling is carried out to digital phase detection and become possibility, digital circuit reliability of operation is subject to the impact of the environmental factors such as temperature smaller, applies the accuracy that suitable algorithm can improve phase demodulation.

In digital received system, analog input signal s (t) is carried out to AD and be converted to digital signal s (n), digital signal is sent in digital processing device (as FPGA) and goes to process, the digital signal that sampling is obtained is processed through Digital Down Convert, obtain base band video i/q signal, in i/q signal, comprised the amplitude and the phase information that receive signal.If receiving the baseband signal of signal is s _b(n), its in-phase component signal I (n) and orthogonal component signal Q (n) can be expressed as:

According to trigonometric function relation, there is signal s _b(n) amplitude A (n) and phase place mathematical relationship:

$A\left(n\right)=\sqrt{I{\left(n\right)}^2+Q{\left(n\right)}^2}$

Like this, after carrying out quadrature demodulation to digital quadrature signal, numeric field just can obtain amplitude and the phase information of baseband signal.

In above formula square, evolution and arctangent cp cp operation more complicated, in digital signal processor, realizing can be more difficult.Cordic algorithm is to be proposed by J.Voilder in nineteen fifty-nine, when solving the mathematical operation of the complexity such as trigonometric function, exponential function and surmount function, does not need hardware multiplier, only needs displacement, add/subtraction and simple look up table operations.Due to these advantages, in recent years, the mathematical theory of cordic algorithm and practical application realize studied and development always, and obtained application in field widely, for example be applied to the FFT in Digital Signal Processing, the DCT in image compression, the aborning DDS of digital waveform etc.

Cordic algorithm has three kinds of rotating coordinate systems: linear coordinate system, circle coordinates system and hyperbolic coordinate system.It has two kinds of rotary modes: rotary mode and arrow pattern.Their rotation formula has been unified in a formula, and formula is as follows:

$\left\{\begin{array}{c}{x}_{i+1}=x_i-m\·{\mathrm{\δ}}_i\·y_i\·2^{-i}\\ y_{i+1}=y_i+{\mathrm{\δ}}_i\·x_i\·2^{-i}\\ z_{i+1}=z_i-{\mathrm{\δ}}_i\·{\mathrm{\ϵ}}_i\end{array}\right.$

Wherein, parameter m represents work system, and m=1 is polling system, and m=0 is linear system, and m=-1 is hyperbolic systems; Direction of rotation δ _ivalue in each rotary course, the value of the result of being rotated by the last time determines.Choose reasonable m, ε _iand initial condition { x ₀, y ₀, z ₀just can realize the computing of different mathematical functions.

When selecting the circumference rotary system of m=1, δ _ivalue by the y that rotates output _ithe symbol of value decide, i.e. the arrow pattern of cordic algorithm, ${\mathrm{\&delta;}}_i=\left\{\begin{array}{c}-1,y_i\&GreaterEqual;0\\ +1,y_i<0\end{array}\right.,$ Select initial condition $\left\{\begin{array}{c}{x}_0=I\left(n\right)\\ y_0=Q\left(n\right)\\ z_0=0\end{array}\right.,$ Select every grade of fixedly anglec of rotation ε _i=arctan (2 ^-i), i=0 wherein, 1,2 ..., N-1, wherein N represents the progression of cordic algorithm rotation.After rotation N time, y _itrend towards 0, can obtain following operation result:

$x_N=K*\sqrt{I{\left(n\right)}^2+Q{\left(n\right)}^2}$

$z_N=\arctan \left(\frac{Q\left(n\right)}{I\left(n\right)}\right)$

Wherein, $K=\sqrt{1^2+{\left(2^0\right)}^2}\&CenterDot;\sqrt{1^2+{\left(2^{-1}\right)}^2}\&CenterDot;\sqrt{1^2+{\left(2^{-2}\right)}^2}...\sqrt{1^2+{\left(2^{-2(N-1)}\right)}^2}\&ap;1.6468,$ Amplitude gain for cordic algorithm rotation.When number of times one timing of rotation, K is definite value; Owing to being subject to the fixedly restriction of the anglec of rotation, maximum occurrences scope be about (99.88 °, 99.88 °).

Although can realize well the function of being carried out phase demodulation by orthogonal signalling according to above-mentioned rotation formula in digital signal processor.In theory, when the number of times of iteration is abundant, the amplitude and the phase place that obtain approach theoretical value.But, due to when the cordic algorithm Digital Implementation, the figure place that amplitude and phase place represent is all limited, there is truncated error, the accuracy of phase demodulation also can be affected like this, and particularly, in the situation that the mould value of input orthogonal signalling I (n) and Q (n) is less, the impact that the result of amplitude is subject to is little, identified result but there will be larger error, and phase demodulation accuracy can not meet the demands.

Summary of the invention

The problem existing in order to solve background technology, the present invention aims to provide digital phase detecting method and the device based on improved cordic algorithm, has solved in the situation that input orthogonal signalling mould value is less, and identified result error is large, the problem that phase demodulation accuracy is low.

In order to realize above-mentioned technical purpose, technical scheme of the present invention is:

A digital phase detection device based on improved cordic algorithm, comprises the n level module connecting successively, the iterations that n is improved cordic algorithm and n>=1, modular structures at different levels are identical, all there are 3 inputs and 3 outputs, 3 outputs of 3 inputs one-level module after corresponding connection of previous stage module, and modules at different levels include the first～tri-register, the the first～tri-adder, the first shift unit, the second shift unit and an anglec of rotation memory, wherein, the input of the first～tri-register is respectively as the first～tri-input of this grade of module, the output of the first～tri-adder is respectively as the first～tri-output of this grade of module, and the output of the first register connects respectively the first input end of first adder and the second input of second adder, the output of the second register connects the second input of first adder via the first shift unit, the output of described the second register also connects the first input end of second adder via the second shift unit, the output of the output of the 3rd register and anglec of rotation memory is connected respectively first of the 3rd adder, two inputs, the the first～tri-input of described first order module is for initial condition I (n), the Q (n), 0 of the corresponding input of difference base band video i/q signal, and the first～tri-output of n level module is respectively used to export iteration result x _n, Δ y _n, z _n, the first shift unit in m level module is carried out 2 (m-1)-1 bit manipulations that move to right, and its second shift unit is carried out 1 bit manipulation that moves to left, wherein, and m=1,2,3 ..., n-1.

The present invention also comprises the digital phase detecting method based on said apparatus, comprises following steps:

(1) analog input signal is carried out to analog-to-digital conversion, obtain corresponding sampled digital signal;

(2) sampled digital signal is carried out to Digital Down Convert processing, obtain base band video i/q signal s _b(n), thus obtain its in-phase component signal I (n) and orthogonal component signal Q (n);

(3): definition respectively $\begin{array}{cc}\left\{\begin{array}{c}{x}_0=I\left(n\right)\\ {\mathrm{\&Delta;y}}_0=Q\left(n\right),\\ z_0=0\end{array}\right.& {\mathrm{\&delta;}}_0=\left\{\begin{array}{c}-1,{\mathrm{\&Delta;y}}_0\&GreaterEqual;0\\ +1,{\mathrm{\&Delta;y}}_0<0\end{array}\right.\end{array},$ ε ₀=π/4, and by (x ₀, Δ y ₀, z ₀), δ ₀, ε ₀as the initial condition of improved cordic algorithm, initial direction of rotation, initial rotation angle degree, carry out interative computation respectively, until iteration result meets required precision, from this iteration result, extract the phase information of analog input signal; Described improved cordic algorithm is:

$\left\{\begin{array}{c}{x}_{i+1}=x_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&Delta;y}}_i\&CenterDot;2^{-i}\&CenterDot;2^{-(i-1)}\\ {\mathrm{\&Delta;y}}_{i+1}=2\&CenterDot;{\mathrm{\&Delta;y}}_i+{\mathrm{\&delta;}}_i\&CenterDot;x_i\\ z_{i+1}=z_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&epsiv;}}_i\end{array}\right.$

In above formula, i=0,1,2,3 ..., when i>=1, (x _i, Δ y _i, z _i) be the space vector of i level rotation output, δ _ibe i level direction of rotation and ${\mathrm{\&delta;}}_i=\left\{\begin{array}{c}-1,{\mathrm{\&Delta;y}}_i\&GreaterEqual;0\\ +1,{\mathrm{\&Delta;y}}_i<0\end{array}\right.,$ ε _ibe the i level anglec of rotation and ε _i=arctan (2 ^-i).

The beneficial effect that adopts technique scheme to bring:

In the present invention, improve in the algorithm of CORDIC direction of rotation δ _ivalue no longer according to y _isymbol, but according to Δ y _ivalue, Δ y _iy _icarry out 2 ⁱvalue after multiple value is amplified, when not there is sign bit and overflowing, Δ y _iwith y _isign bit is consistent, but at y _iapproach in 0 situation Δ y _iretain more number of significant digit, can be good at preserving lower y _ithe symbol of component, while improving next stage iteration, the accuracy of direction of rotation judgement, finally makes the accuracy of phase demodulation improve.

Accompanying drawing explanation

Fig. 1 is the hardware structure diagram that cordic algorithm flowing water of the present invention is realized.

Fig. 2 is the hardware structure diagram of realizing the computing of improved cordic algorithm one-level in the present invention.

Fig. 3 is the simulation result figure of the cordic algorithm before improving under the first input condition.

Fig. 4 is the simulation result figure of the cordic algorithm after improving under the first input condition.

Fig. 5 is the simulation result figure of the cordic algorithm before improving under the second input condition.

Fig. 6 is the simulation result figure of the cordic algorithm after improving under the second input condition.

Embodiment

Below with reference to accompanying drawing, technical scheme of the present invention is elaborated.

Cordic algorithm is commonly used to carry out digital phase detection, and traditional digital phase detecting method based on cordic algorithm is:

(1) analog input signal is carried out to analog-to-digital conversion, obtain corresponding sampled digital signal;

(2) sampled digital signal is carried out to Digital Down Convert processing, obtain base band video i/q signal s _b(n), thus obtain its in-phase component signal I (n) and orthogonal component signal Q (n);

(3) definition respectively $\begin{array}{cc}\left\{\begin{array}{c}{x}_0=I\left(n\right)\\ {\mathrm{\&Delta;y}}_0=Q\left(n\right),\\ z_0=0\end{array}\right.& {\mathrm{\&delta;}}_0=\left\{\begin{array}{c}-1,{\mathrm{\&Delta;y}}_0\&GreaterEqual;0\\ +1,{\mathrm{\&Delta;y}}_0<0\end{array}\right.\end{array},$ ε ₀=π/4, and by (x ₀, Δ y ₀, z ₀), δ ₀, ε ₀as the initial condition of traditional C ORDIC algorithm, initial direction of rotation, initial rotation angle degree, carry out interative computation respectively, until iteration result meets required precision, from this iteration result, extract the phase information of analog input signal.Described traditional C ORDIC algorithm is:

$\left\{\begin{array}{c}{x}_{i+1}=x_i-{\mathrm{\&delta;}}_i{\&CenterDot;y}_i\&CenterDot;2^{-i}\\ y_{i+1}=y_i+{\mathrm{\&delta;}}_i\&CenterDot;x_i\&CenterDot;2^{-i}\\ z_{i+1}=z_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&epsiv;}}_i\end{array}\right.---\left(1\right)$

In formula (1), i=0,1,2,3 ..., when i>=1, (x _i, y _i, z _i) be the space vector of i level rotation output, δ _ibe i level direction of rotation, ε _ibe the i level anglec of rotation and ε _i=arctan (2 ^-i), δ wherein _iwith y _imeet relation: δ _i=-sign (y _i), ${\mathrm{\&delta;}}_i=\left\{\begin{array}{c}-1,y_i\&GreaterEqual;0\\ +1,y_i<0\end{array}\right..$

The present invention compares with conventional digital phase detecting method, and improvements are to adopt improved cordic algorithm to replace the traditional C ORDIC algorithm in above-mentioned steps (3).Improved cordic algorithm obtains through traditional cordic algorithm conversion, first at y _i+1=y _i+ δ _ix _i2 ^-iboth members be multiplied by 2 simultaneously ⁱ,,

$\left\{\begin{array}{c}{x}_{i+1}=x_i-{\mathrm{\&delta;}}_i\&CenterDot;y_i\&CenterDot;2^{-i}\\ 2^i\&CenterDot;y_{i+1}=2^i\&CenterDot;y_i+2^i\&CenterDot;{\mathrm{\&delta;}}_i\&CenterDot;x_i\&CenterDot;2^{-i}\\ z_{i+1}=z_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&epsiv;}}_i\end{array}\right.---\left(2\right)$

Make again Δ y _i=2 ^i-1y _i, Δ y _i+1=2 ⁱy _i+1, in substitution formula (2),,

$\left\{\begin{array}{c}{x}_{i+1}=x_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&Delta;y}}_i\&CenterDot;2^{-i}\&CenterDot;2^{-(i-1)}\\ {\mathrm{\&Delta;y}}_{i+1}=2\&CenterDot;{\mathrm{\&Delta;y}}_i+{\mathrm{\&delta;}}_i\&CenterDot;x_i\\ z_{i+1}=z_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&epsiv;}}_i\end{array}\right.---\left(3\right)$

Formula (3) is improved cordic algorithm, in this algorithm, and definition respectively $\left\{\begin{array}{c}{x}_0=I\left(n\right)\\ {\mathrm{\&Delta;y}}_0=Q\left(n\right)\\ z_0=0\end{array}\right.,$ ${\mathrm{\&delta;}}_0=\left\{\begin{array}{c}-1,{\mathrm{\&Delta;y}}_0\&GreaterEqual;0\\ +1,{\mathrm{\&Delta;y}}_0<0\end{array}\right.,$ ε ₀interative computation is carried out as the initial condition of improved cordic algorithm, initial direction of rotation, initial rotation angle degree in=π/4, until iteration result meets required precision, extracts the phase information of analog input signal from this iteration result.δ _ino longer according to y _ivalue, but according to Δ y _ivalue: δ _i=-sign (Δ y _i), ${\mathrm{\&delta;}}_i=\left\{\begin{array}{c}-1,{\mathrm{\&Delta;y}}_i\&GreaterEqual;0\\ +1,{\mathrm{\&Delta;y}}_i<0\end{array}\right..$ Can increase the number of significant digit of data representation like this, reduce the mistake of symbol decision, make direction of rotation correct judgment, improve last identified result.

As depicted in figs. 1 and 2, the digital phase detection device based on improved cordic algorithm of the present invention, comprises the n level module connecting successively, the iterations that n is improved cordic algorithm and n>=1, modular structures at different levels are identical, all there are 3 inputs and 3 outputs, 3 outputs of 3 inputs one-level module after corresponding connection of previous stage module, and modules at different levels include the first～tri-register, the the first～tri-adder, the first shift unit, the second shift unit and an anglec of rotation memory, wherein, the input of the first～tri-register is respectively as the first～tri-input of this grade of module, the output of the first～tri-adder is respectively as the first～tri-output of this grade of module, and the output of the first register connects respectively the first input end of first adder and the second input of second adder, the output of the second register connects the second input of first adder via the first shift unit, the output of described the second register also connects the first input end of second adder via the second shift unit, the output of the output of the 3rd register and anglec of rotation memory is connected respectively first of the 3rd adder, two inputs, the the first～tri-input of described first order module is for initial condition I (n), the Q (n)/2,0 of the corresponding input of difference base band video i/q signal, and the first～tri-output of n level module is respectively used to export iteration result x _n, Δ y _n, z _n, the first shift unit in m level module is carried out 2 (m-1)-1 bit manipulations that move to right, and its second shift unit is carried out 1 bit manipulation that moves to left, wherein, and m=1,2,3 ..., n-1.

In the present embodiment, the programming of the former algorithm of CORDIC and improvement algorithm of the present invention and functional simulation complete in the hardware logic development platform software I SE12.4 of Xilinx.The processing of emulation the data obtained, contrast and mapping are completed on software MATLAB7.10.Some design parameters of the present embodiment are as follows: with flowing structure, realize the rotation of 15 grades of CORDIC arrow patterns, the Output rusults x of input I (n) and Q (n) data and rotations at different levels _i, y _iand z _iall adopt the fixed binary complement code form of 16-bit to represent.

Fig. 3 and Fig. 4 are respectively cordic algorithm and improve the simulation result figure after front and improvement.Their emulation initial inputs are the same, be by I (n)=Q (n)=5*x (x=1 wherein, 2 ..., 200) this 200 logarithm value changes into 16-bit binary data as input signal.Owing to being the data that 16-bit represents, so in the situation that considering uncompensation CORDIC rotation gain and preventing that end product from overflowing, maximum input data are so maximum 1000 input signal can be regarded as small-signal.In ISE functional simulation, by simulation clock (100MHz), read in this group data, as initial I (n) and Q (n) (I (n)=Q (n)) data, carry out emulation.Record respectively the simulation result of these two kinds of realizations and they are imported in MATLAB, Fig. 3 is before improving, and Fig. 4 is that after improving, the coordinate system range of two figure is consistent.According to theory, calculate, due to this 200 pairs of data I (n)=Q (n), the identified result calculating should all equate, and equals binary code word 8192, changes into the number of degrees and is expressed as as can be seen from Figure 3, identified result is fluctuation up and down near 8192, and input data are less, fluctuates larger, and along with data increase, fluctuation reduces gradually; From Fig. 4, can obviously find out, when input data are very little, fluctuation is just few, and phase demodulation accuracy is significantly improved.

Fig. 5 and Fig. 6 are before cordic algorithm improves under another kind of input condition and improve post-layout simulation results exhibit figure.This input data are in the situation that keeping I (n)=100, the numerical value of Q (n) input is changed to 1000 from 100 inputs, what Fig. 5 was corresponding is before cordic algorithm improves, what Fig. 6 was corresponding is after algorithm improves, the coordinate system range of two figure is consistent, can clearly find out that algorithm improves phase demodulation accuracy afterwards and was greatly improved before improving from figure.

Cordic algorithm before improving and after improving is after the hardware logic design platform ISE12.4 of Xilinx company hardware language is realized and be comprehensive, and the contrast of the main hardware resource of consumption is as shown in table 1.As can be seen from Table 1, how many algorithms after improvement does not increase with former algorithm on resource is used, and even on Slice Registers resource consumption, reduces to some extent.

Table 1

?	Before improvement	After improvement
			Slice?Registers	706	690
Slice?LUTs	780	868

Above embodiment only, for explanation technological thought of the present invention, can not limit protection scope of the present invention with this, every technological thought proposing according to the present invention, and any change of doing on technical scheme basis, within all falling into protection range of the present invention.

Claims (2)

1. the digital phase detection device based on improved cordic algorithm, is characterized in that: comprise the n level module connecting successively, the iterations that n is improved cordic algorithm and n>=1, modular structures at different levels are identical, all there are 3 inputs and 3 outputs, 3 outputs of 3 inputs one-level module after corresponding connection of previous stage module, and modules at different levels include the first～tri-register, the the first～tri-adder, the first shift unit, the second shift unit and an anglec of rotation memory, wherein, the input of the first～tri-register is respectively as the first～tri-input of this grade of module, the output of the first～tri-adder is respectively as the first～tri-output of this grade of module, and the output of the first register connects respectively the first input end of first adder and the second input of second adder, the output of the second register connects the second input of first adder via the first shift unit, the output of described the second register also connects the first input end of second adder via the second shift unit, the output of the output of the 3rd register and anglec of rotation memory is connected respectively first of the 3rd adder, two inputs, the the first～tri-input of described first order module is for initial condition I (n), the Q (n), 0 of the corresponding input of difference base band video i/q signal, and the first～tri-output of n level module is respectively used to export iteration result x _n, Δ y _n, z _n, the first shift unit in m level module is carried out 2 (m-1)-1 bit manipulations that move to right, and its second shift unit is carried out 1 bit manipulation that moves to left, wherein, and m=1,2,3 ..., n-1.

2. the digital phase detecting method based on the digital phase detection device based on improved cordic algorithm claimed in claim 1, comprises following steps:

(1) analog input signal is carried out to analog-to-digital conversion, obtain corresponding sampled digital signal;

(2) sampled digital signal is carried out to Digital Down Convert processing, obtain base band video i/q signal s _b(n), thus obtain its in-phase component signal I (n) and orthogonal component signal Q (n); It is characterized in that: also comprise step (3): definition respectively $\begin{array}{cc}\left\{\begin{array}{c}{x}_0=I\left(n\right)\\ {\mathrm{\&Delta;y}}_0=Q\left(n\right),\\ z_0=0\end{array}\right.& {\mathrm{\&delta;}}_0=\left\{\begin{array}{c}-1,{\mathrm{\&Delta;y}}_0\&GreaterEqual;0\\ +1,{\mathrm{\&Delta;y}}_0<0\end{array}\right.\end{array},$ ε ₀=π/4, and by (x ₀, Δ y ₀, z ₀), δ ₀, ε ₀as the initial condition of improved cordic algorithm, initial direction of rotation, initial rotation angle degree, carry out interative computation respectively, until iteration result meets required precision, from this iteration result, extract the phase information of analog input signal; Described improved cordic algorithm is:

$\left\{\begin{array}{c}{x}_{i+1}=x_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&Delta;y}}_i\&CenterDot;2^{-i}\&CenterDot;2^{-(i-1)}\\ {\mathrm{\&Delta;y}}_{i+1}=2\&CenterDot;{\mathrm{\&Delta;y}}_i+{\mathrm{\&delta;}}_i\&CenterDot;x_i\\ z_{i+1}=z_i-{\mathrm{\&delta;}}_i\&CenterDot;{\mathrm{\&epsiv;}}_i\end{array}\right.$

In above formula, i=0,1,2,3 ..., when i>=1, (x _i, Δ y _i, z _i) be the space vector of i level rotation output, δ _ibe i level direction of rotation and ${\mathrm{\&delta;}}_i=\left\{\begin{array}{c}-1,{\mathrm{\&Delta;y}}_i\&GreaterEqual;0\\ +1,{\mathrm{\&Delta;y}}_i<0\end{array}\right.,$ ε _ibe the i level anglec of rotation and ε _i=arctan (2 ^-i).