CN101515913B - Fixed loop control method based on additions and shifts - Google Patents

Abstract

The invention discloses a fixed-point loop control method based on shift and addition. Aiming at the requirement of using low-end processor or hardware description language to realize the loop control in the baseband signal processing of the spread spectrum communication receiver, the present invention implements the loop phase detector using the fixed-point algorithm that can be realized by shifting and adding, and the loop filter Comprehensive consideration of the device coefficient and NCO gain, which is approximately an integer power of 2, completes loop filtering and generates new carrier frequency control words and code frequency control words through shifting and addition. The invention not only greatly reduces the calculation amount of the loop control, but also basically does not lose the loop tracking precision through reasonable selection of the bit width.

Description

A fixed-point loop control method based on shift and addition

technical field

The invention relates to the field of loop control of related channels of spread spectrum communication receivers, in particular, the invention relates to a fixed-point loop control method based on shift and addition.

Background technique

The spread spectrum (spread spectrum) communication system is an ideal communication system based on the theoretical basis of C.E. Shannon's information theory. It refers to a communication method in which the radio frequency bandwidth used to transmit information is much larger than the bandwidth of the information itself. The spread spectrum communication system has many unique advantages such as strong anti-interference, low interception rate, code division multiple access, signal concealment, strong confidentiality, ranging and easy networking. It has been widely used in communication, navigation, radar, positioning , ranging, remote control, aerospace, electronic countermeasures, mobile communications and other fields.

The correlation channel is one of the core processing modules of the direct sequence spread spectrum communication receiver, and its research focus is mainly on the tracking of signal carrier and pseudo code. The spread-spectrum signal received by the antenna is amplified by a low-noise amplifier, down-converted to an intermediate frequency, and then sampled by an analog-to-digital converter (ADC) to become a digital signal. When the spread-spectrum receiver finishes capturing the spread-spectrum signal, it puts the captured code phase and carrier Doppler into the relevant channel, and begins to accurately track the carrier phase and pseudo-code phase.

The correlation channel is composed of correlator, loop control, data extraction, observation extraction and other modules. The correlator is generally implemented by a Field Programmable Gate Array (FPGA) or an Application Specific Integrated Circuit (ASIC), which completes the stripping of the carrier and pseudo code, and realizes pre-detection integration. The loop control module implements phase detection, filtering and generation of new carrier frequency control words and code frequency control words according to the lead, instant and lag accumulation sums of the in-phase (I) path and quadrature (Q) path output by the correlator. Feedback control of the associated channel. When the loop is locked, the bit synchronization and frame synchronization of the data can be performed, as well as the extraction of observations such as pseudorange and Doppler frequency.

The loop control structure of the carrier tracking loop and the code tracking loop is the same, and they are composed of three parts: a phase detector, a filter, and a numerically controlled oscillator (NCO). The carrier tracking loop adopts the Costas loop which is insensitive to data modulation to realize the precise tracking of the carrier phase. A well-designed carrier tracking loop should first close the loop with a frequency-locked loop (FLL) that works in a wide frequency band and is more robust to dynamics, then gradually transition to a large-bandwidth Costas loop, and finally increase the bandwidth of the Costas loop. narrowed to steady state mode of operation. The code tracking loop uses a delay-locked loop (DLL) to realize accurate tracking of the pseudo-code phase. Since the carrier loop-assisted code loop technology can eliminate all the dynamics in the code loop, the bandwidth of the code loop can be narrowed relative to the bandwidth of the carrier loop to improve the pseudo-range accuracy.

At present, there are very mature conclusions about the theoretical analysis of loop control and the corresponding performance indicators. However, floating-point loop control is generally used in the implementation. Although the precision will not be lost, this makes the requirements for the processor higher, and it is difficult to implement it directly in hardware with a hardware description language.

Contents of the invention

The technical problem to be solved by the present invention is: Aiming at the requirement of using low-end processor or hardware description language to realize the loop control in the baseband signal processing of the spread spectrum communication receiver, a fixed-point loop control method based on shift and addition is proposed, It is achieved through the following steps:

a. After the correlator completes the integral accumulation, it outputs 6 accumulation results, and the loop control module realizes the control of the carrier tracking loop and the code tracking loop according to the 6 accumulation results;

b. Use the coordinate rotation digital calculation (Cordic) algorithm to realize the two-quadrant arc tangent (atan), complete the work of the carrier loop phase detector, that is, atan (Q _P /I _P ), and form the carrier loop phase detector error x(n);

c. For the carrier loop phase detection error x(n), carrier loop intermediate variables u(n-1) and u(n-2), after appropriate shift and addition operations, the carrier loop filter is realized to form a carrier loop filter The device outputs z(n) and the new carrier ring intermediate variable u(n);

d. The carrier loop filter output z (n), plus the carrier intermediate frequency frequency control word, forms a new carrier frequency control word, and feeds back to the tracking loop to control the carrier loop;

e. Update the intermediate variable of the carrier loop for use in the next loop control, so far, the loop control of the carrier loop is completed;

f. Using an approximate algorithm to calculate the envelope, respectively complete the calculation of the lead and lag accumulation and the envelope;

g. Adopt the binary division module based on shift and addition to complete the phase detector work of the code ring to form the code ring phase detection error x(n);

h. For the code ring phase detection error x(n) and the code ring intermediate variable u(n-1), after appropriate shifting and addition operations, the code ring filter is realized to form the code ring filter output z(n) and New code ring intermediate variable u(n);

i. code loop filter output z (n), add carrier loop filter output z (n) divided by the carrier auxiliary parameter that scale factor obtains, add code intermediate frequency frequency control word again, form new code frequency control word, Feedback to the tracking loop to control the code loop;

j. Update the intermediate variable of the code loop for use in the next loop control, so far, the loop control of the code loop is completed.

In the above step c, the carrier loop filter is a third-order filter, which is realized by direct type II, and the filter coefficient and NCO gain are considered comprehensively, which is approximately an integer power of 2, and is realized by shifting, and the number of shifts can be Determined according to the designed loop bandwidth.

In the above step h, the code ring filter is a second-order filter, which is realized by direct type II, and the filter coefficient and NCO gain are considered comprehensively, which is approximately an integer power of 2, and is realized by shifting, and the number of shifts can be Determined according to the designed loop bandwidth.

Compared with the prior art, the biggest feature of the present invention is that in the whole loop control process, all operations are simplified to a series of shift and addition operations, and the tracking accuracy is basically not lost through reasonable selection of the bit width. This makes the implementation of the loop control can adopt a very low-end processor, or can also be directly implemented in hardware with a hardware description language. Therefore, the present invention has the advantages of low calculation amount, simple implementation mode and no influence on loop tracking precision.

Description of drawings

The above-mentioned and other objects and features of the present invention will become clearer through the following detailed description in conjunction with the accompanying drawings, wherein:

Figure 1 is a typical block diagram of the relevant channels of a spread spectrum communication receiver.

Fig. 2 is the implementation method of the fixed-point loop control in the relevant channel.

Figure 3 is an iterative block diagram of the Cordic algorithm.

Figure 4 is a block diagram of the digital filter structure of the carrier tracking loop.

Fig. 5 is a structural block diagram of implementing binary division by shifting and adding.

Figure 6 is a block diagram of the digital filter structure of the code tracking loop.

Detailed ways

The advantages and features of the present invention and the method of realization can be more easily understood with reference to the following detailed description of the exemplary embodiments in conjunction with the accompanying drawings.

Fig. 1 is a typical block diagram of correlation channels widely used in spread spectrum communication receivers at present. After the sampling data enters the relevant channel, it is firstly multiplied with the local sine-cosine carrier to realize carrier stripping to generate in-phase (I) and quadrature (Q) data, and then respectively combined with the locally generated lead (E), instant (P) and Lag (L) recurring codes are multiplied to realize code stripping, and integral accumulation is carried out. The loop control module generates a new carrier frequency control word and code frequency control word according to the integration and accumulation results of the correlator, and performs feedback control on the tracking loop.

Figure 2 is the realization method of the fixed-point loop control in the relevant channel, which is divided into two parts: the carrier loop control and the code loop control. It is achieved through the following steps.

a. After the correlator completes the integration and accumulation, it outputs 6 accumulation results, namely in-phase lead (I _E ), in-phase instant (I _P ), in-phase lag (I _L ), quadrature lead (Q _E ), quadrature instant (Q _P ), quadrature lag (Q _L ), the carrier tracking loop is controlled by I _P and Q _P , and the code loop is controlled by I _E , I _L , Q _E and Q _L.

b. Use the Cordic algorithm to realize the two-quadrant arc tangent atan, and complete the work of the carrier loop phase detector, that is, atan(Q _P /I _P ), to form the carrier loop phase detector error x(n). The data range of the phase detection result is [-π/2, π/2], and it needs to be represented by the Q format notation when using fixed-point implementation, that is, x(n) is the expanded phase detection result, to be After filtering, the same number of digits can be discarded. The Q format of x(n) is determined by the Q format of the lookup table content in the Cordic algorithm. Generally, Q30 is used, but when x(n) is input to the loop filter, using Q30 will occupy too large a bit width, and it can be Intercept to Q5, no matter how small it will affect the accuracy of the carrier loop.

c. The carrier loop filter is implemented by a series of shifts and additions to form the carrier loop filter output z(n) and the new carrier loop intermediate variable u(n). The carrier loop filter uses a third-order filter, which can track the acceleration stably. The output z(n) of the carrier loop filter consists of a total of 6 additions, which are:

The phase error x(n) of the carrier loop is shifted to the left by a bit;

The phase error x(n) of the carrier loop is shifted to the left by b bits;

The phase error x(n) of the carrier loop is shifted to the left by c bits;

The intermediate variable u(n-1) is shifted to the left by (a+2) bits at a moment before the carrier loop;

The intermediate variable u(n-1) is shifted to the left by (b+1) bits at a moment before the carrier loop;

The intermediate variable u(n-2) in the first two moments of the carrier loop is shifted to the left by (b+1) bits;

The new carrier ring intermediate variable u(n) is composed of three additions, which are:

phase error x(n);

The intermediate variable u(n-1) at the moment before the carrier loop is shifted left by 1 bit;

The intermediate variable u(n-2) in the first two moments of the carrier loop is negative;

Among them, a, b, and c all refer to the amount of shifting, positive means shifting to the left, and negative means shifting to the right.

d. Carrier loop filter output z(n) discards the number of digits in the phase detection time expansion, and adds the carrier intermediate frequency frequency control word to form a new carrier frequency control word, which is fed back to the tracking loop to control the carrier loop .

e. Update the intermediate variable of the carrier loop, update u(n-2) to u(n-1), and update u(n-1) to the newly formed u(n), for use in the next loop control. So far, the loop control of the carrier loop is completed.

f. Use the approximate algorithm to calculate the envelope, and complete the calculation of the lead and lag accumulation and the envelope respectively, that is, to form $\mathrm{E.}=\sqrt{I_{\mathrm{E.}}^2+Q_{\mathrm{E.}}^2},$ $L=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="I\; L"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">I</figure-callout>}}_L^{}+{\mathrm{<figure-callout\; id="2"\; label="Q\; L"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">Q</figure-callout>}}_L^{}}.$

g. Use the binary division module based on shift and addition to complete the phase detector work of the code ring to form the phase detection error x(n) of the code ring, namely

$\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}}$

Similar to the carrier loop phase detector, since the result range of (E-L)/(E+L) is [-1, 1], it also needs to be expressed in Q format notation, that is, the output result of the phase detector is For the expanded data, the same number of digits can be discarded after filtering. The specific number of extended bits is determined to be 7 by simulation. In addition, the division by 2 operation of the code ring phase detector can be omitted for the time being, and it will be performed together when truncation is performed after filtering.

h. Using a series of shifts and additions to realize the code ring filter to form the code ring filter output z(n) and the new code ring intermediate variable u(n). Since the carrier loop will assist the code loop to eliminate all dynamics, the code loop filter uses a second-order filter. The output z(n) of the code ring filter consists of a total of 3 additions, which are:

The phase error x(n) of the code ring is shifted to the left by d bits;

The phase error x(n) of the code ring is shifted to the left by e bits;

The intermediate variable u(n-1) is shifted to the left by (d+1) bits at a moment before the code ring;

The new code ring intermediate variable u(n) is composed of two additions, which are:

Code ring phase error x(n);

The intermediate variable u(n-1) at the moment before the code ring;

Among them, d and e both refer to the number of shifts, positive for left shift, negative for right shift.

i. After the code loop filter output z(n) discards the number of digits in the phase detection time expansion, add the carrier auxiliary parameter obtained by dividing the carrier loop filter output z(n) by the scale factor, plus the code intermediate frequency frequency The control word, that is to form a new code frequency control word, is fed back to the tracking loop to control the code loop.

j updates the intermediate variable of the code loop, and updates u(n-1) to the newly formed u(n), which is used for the next loop control. So far, the code loop loop control is completed.

For the above step b, Fig. 3 is an iterative block diagram of the Cordic algorithm. The Cordic algorithm is the coordinate rotation digital calculation method (Coordinate Rotation Digital Computer), which can perform many mathematical operations, such as sine, cosine, complex multiplication, arctangent, and modulus. When using the Cordic algorithm to calculate the two-quadrant arc tangent, it works in the vector mode, that is

x _i+1 = x _i -y _i ·d _i ·2 ^-i

y _i+1 ＝y _i +x _i ·d _i ·2 ^-i

z _i+1 = z _i -d _i ·tan ^-1 (2 ^-i )

Wherein, when y _i <0, d _i =1, and when y _i >0, d _i =-1. After several iterations, we get

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

y _n =0

z _n =z ₀ +tan ^-1 (y ₀ /x ₀ )

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.647</span>}$

In the above algorithm, the operation of tan ^-1 (2 ^-i ) can be realized by using table lookup, and the operation of multiplying by 2 ^-i can be realized by shifting, so that the process of calculating atan is realized by addition, shifting and table lookup. Since the rotation angle of the Cordic algorithm is between -π/2 and π/2, when using it to calculate atan, it must be guaranteed that x>0. When x<0, you need to invert both x and y first, and then perform the operation.

For the above step c, the design method of the shift quantities a, b, and c in the carrier tracking loop filter is described below. Figure 4 is a block diagram of the digital filter structure of the carrier tracking loop, and its mathematical expression is

y(n)=2y(n-1)-y(n-2)+b0*x(n)+b1*x(n-1)+b2*x(n-2)

b0, b1 and b2 are determined by the loop parameters, namely

b0=k1+k2+k3

b1=2*(k1-k3)

b2=k1-k2+k3

in

$\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2009100804609E00021.png,H2009100804609E00033.png"\; state="\{\{state\}\}">k</figure-callout>}1=\frac{{\mathrm{\&omega;}}_0^3{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">T</figure-callout>}}^2}{4},$ $\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">k</figure-callout>}2=\frac{a_3{\mathrm{\&omega;}}_0^2\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">T</figure-callout>}}{2},$ k3＝b ₃ ω ₀

a3=1.1, b3=2.4;

T is the integral accumulation time;

ω ₀ is the natural circular frequency of the loop, and its size is determined by the loop bandwidth.

When implementing the filter in a fixed-point manner, first change its structure to a direct Type II implementation, that is,

u(n)=x(n)+2u(n-1)-u(n-2)

y(n)=b0*u(n)+b1*u(n-1)+b2*u(n-2)

=(k1+k2+k3)*u(n)+2*(k1-k3)*u(n-1)+(k1-k2+k3)*u(n-2)

＝k1*[u(n)+2*u(n-1)+u(n-2)]+k2*[u(n)-u(n-2)]

+k3*[u(n)-2*u(n-1)+u(n-2)]

＝k1*[x(n)+4*u(n-1)]+k2*[x(n)+2*u(n-1)-2*u(n-2)]

+k3*x(n)

The carrier loop NCO is implemented with an Nbit accumulator. For the NCO gain of the carrier loop, its unit is radiansper second per unit, which means that each controlled unit represents how many radians physically in 1 second, that is

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}$

Since the carrier NCO has a gain K, the carrier frequency control word fed back to the relevant channel should be divided by the gain, that is

z(n)=y(n)/K

＝k1/K*[x(n)+4*u(n-1)]+k2/K*[x(n)+2*u(n-1)-2*u(n-2)]

+k3/K*x(n)

＝h1*[x(n)+4*u(n-1)]+h2*[x(n)+2*u(n-1)-2*u(n-2)]

+h3*x(n)

Approximate h1, h2, and h3 to an integer power of 2, so that multiplication can be realized by shifting. The final implementation of the carrier loop filter is

u(n)=x(n)+[u(n-1)<<1]-u(n-2)

z(n)=[x(n)<<a]+[u(n-1)<<(a+2)]+[x(n)<<b]

+[u(n-1)<<(b+1)]-[u(n-2)<<(b+1)]+[x(n)<<c]

Among them, a, b, and c all refer to the number of shifts, and its size is determined by the loop parameters. When it is positive, it means shifting to the left, and when it is negative, it means shifting to the right.

The output z(n) of the carrier loop filter plus the frequency control word f _i /f _s 2 ^N corresponding to the carrier intermediate frequency is the frequency control word fed back to the carrier loop NCO, and z(n) will also control the code loop Assist.

For the JPL algorithm used in the above step f, it is a simple method for calculating the envelope proposed by the Jet Propulsion Laboratory (JPL), that is, for $A=\sqrt{I^2+{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">Q</figure-callout>}}^2}$ The JPL is approximately

A＝X+1/8Y When X≥3Y

A＝7/8X+1/2Y When X≤3Y

where X=MAX(|I|, |Q|), Y=MIN(|I|, |Q|). The above operation is realized by shifting, that is,

A＝X+(Y＞＞3) When X≥[Y+(Y＜＜1)]

A=X-(X>>3)+(Y>>1) when X≤[Y+(Y<<1)]

For the division used in the above step g and step i, Fig. 5 shows a block diagram for implementing binary division by shifting and adding. Binary division is essentially to compare the divisor with the dividend to see how many divisors there are in the dividend. Therefore, the process of division operation is the process of subtracting the number of divisors from the dividend. In the process of comparison, first align the lowest bit of the divisor with the highest bit of the dividend, and subtract the divisor from the dividend. If it is enough, it means that the high bit of the dividend contains a divisor. Then the switch in the figure is closed, and the divisor is subtracted from the dividend. At the same time, set 1 in the corresponding position of the quotient; otherwise, if the high bit of the dividend does not contain the divisor, and the switch is not closed, set 0 in the corresponding position of the quotient. Then continuously shift the divisor to continue the comparison, and when all the bits are compared, the calculation of the quotient is completed. It should be noted that this divider can only adapt to the case where both the dividend and the divisor are positive numbers. For the case where the dividend or the divisor is a negative number, it needs to be turned into a positive number first, and then the quotient is determined according to the sign bits of the dividend and the divisor sign bit.

For the above step h, the design method of the shift numbers d and e in the code tracking loop filter will be described below. Figure 6 is a block diagram of the digital filter structure of the code tracking loop, and its mathematical expression is

y(n)=y(n-1)+b0*x(n)+b1*x(n-1)

b0 and b1 are determined by the loop parameters, namely

b0=k1+k2

b1=k1-k2

in

$\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2009100804609E00021.png,H2009100804609E00033.png"\; state="\{\{state\}\}">k</figure-callout>}1=\frac{{\mathrm{\&omega;}}_0^2\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">T</figure-callout>}}{2},$ k2＝a ₂ ω ₀

a2=1.414;

T is the integral accumulation time;

ω ₀ is the natural circular frequency of the loop, and its size is determined by the loop bandwidth.

Similar to the carrier loop filter design method, its structure is changed to a direct type II implementation, namely

u(n)=x(n)+u(n-1)

y(n)=(k1+k2)*u(n)+(k1-k2)*u(n-1)

＝k1*[x(n)+2*u(n-1)]+k2*x(n)

The code ring NCO is also realized by Nbit accumulator. For the NCO gain of the code ring, its unit is code per second per unit, which means that each controlled unit represents how many chips physically in 1 second, that is

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}$

The code frequency control word fed back to the relevant channel is

z(n)=y(n)/K=k1/K*[x(n)+2*u(n-1)]+k2/K*x(n)

=h1*[x(n)+2*u(n-1)]+h2*x(n)

Approximate h1 and h2 to an integer power of 2, so that the multiplication operation can be realized by shifting. The final implementation of the code loop filter is

u(n)=x(n)+u(n-1)

z(n)=[x(n)<<d]+[u(n-1)<<(d+1)]+[x(n)<<e]

Among them, d and e both refer to the number of shifts, and their size is determined by the loop parameters. When it is positive, it means shifting to the left, and when it is negative, it means shifting to the right.

The output z(n) of the code loop filter plus the carrier auxiliary parameter obtained by dividing the output z(n) of the carrier loop filter by the scaling factor, plus the frequency control word f _c /f _s 2 ^N corresponding to the code intermediate frequency, It is the frequency control word fed back to the code ring NCO.

Taking the GPS system as an example below, a design example of the shift quantity of the loop filter is given. Assume that the sampling rate of the GPS receiver is fs=5MHz, the integration and accumulation time is T=1ms, and the bit width of the carrier NCO and the code NCO is N=32bit. Firstly, a design example of a carrier loop filter is given.

Suppose the loop bandwidth is designed as Bn=15Hz, then ω ₀ =B _n /0.7845=38.241, then calculate h1, h2 and h3 to get

$\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00033.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">T</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.24</span>}$

$\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">T</figure-callout></span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 27.49</span>}$

$\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 6273.64</span>}$

Approximate h1, h2 and h3 to the integer power of 2, that is, set h1=1/4, h2=32, h3=8192, then invert the loop coefficient, calculate ω ₀ from h1, and then calculate a from h2 and ω _{0 3} , calculate b ₃ from h3 and ω ₀ , and finally calculate the loop bandwidth B _n from a ₃ , b ₃ and ω ₀ , namely

${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00033.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">T</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 19.41</span>}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.24</span>}$

${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.09</span>}$

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 17.62</span>}$

Since h1, h2 and h3 are approximated, all parameters are different from the pre-designed values. Although the parameters a ₃ and b ₃ are not pre-designed 1.1 and 2.4, their values are relatively close to the design values, which only affect the transient response of the loop and have little impact on the steady-state tracking performance of the loop. The loop bandwidth is slightly larger than the design value, which will increase some noise, but it can be changed by modifying h1, h2 and h3. The following table lists different combinations of h1, h2 and h3, the corresponding loop parameters and the number of shifts.

The design method of the code ring is similar to that of the carrier ring. Suppose the loop bandwidth is designed as Bn=1Hz, then ω ₀ =B _n /0.53=1.89, then calculate h1 and h2 to get

$\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00033.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">T</figure-callout></span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.53</span>}$

$\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2291.73</span>}$

Approximate h1 and h2 to the integer power of 2, that is, set h1=1, h2=2048, then invert the loop coefficient, calculate ω ₀ from h1, then calculate a ₂ from h2 and ω ₀ , and finally calculate a 2 from a ₂ and ω ₀ to calculate the loop bandwidth B _n , that is

${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00033.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.53</span>}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="h"\; filenames="H2009100804609E00021.png,H2009100804609E00041.png"\; state="\{\{state\}\}">h</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.56</span>}$

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.84</span>}$

The following table lists different combinations of h1 and h2, the corresponding loop parameters and the number of shifts.

Compared with the prior art, the biggest feature of the present invention is that in the entire loop control process, all operations are simplified to a series of shifting and adding operations, and the tracking accuracy is basically not lost through reasonable selection of bit width. This makes the implementation of the loop control can adopt a very low-end processor, or can also be directly implemented in hardware with a hardware description language. Therefore, the present invention has the advantages of low calculation amount, simple implementation mode and no influence on loop tracking precision.

Claims (3)

1. one kind based on the displacement and the fixed point loop control method of addition, comprises step:

A. correlator is accomplished and is exported 6 accumulation results after integration adds up, and the loop control module realizes the control to carrier tracking loop and code tracking loop according to these 6 accumulation results; 6 accumulation results are the leading (I of homophase _E), the instant (I of homophase _P), the homophase (I that lags behind _L), the leading (Q of quadrature _E), the instant (Q of quadrature _P), the quadrature (Q that lags behind _L);

B. adopt rotation of coordinate numerical calculation Cordic algorithm to realize two quadrant arc tangent atan, accomplish the work of carrier wave ring phase discriminator, i.e. atan (Q _P/ I _P), form carrier wave ring phase demodulation error x (n), wherein I _PFor homophase instant, Q _PFor quadrature instant;

C. to carrier wave ring phase demodulation error x (n), carrier wave ring intermediate variable u (n-1) and u (n-2), after suitable displacement and add operation, realize the carrier wave ring wave filter, form carrier wave ring wave filter output z (n) and new carrier wave ring intermediate variable u (n);

D. carrier wave ring wave filter output z (n) adds carrier wave IF-FRE control word, forms new carrier frequency control word, feeds back to track loop the carrier wave ring is controlled;

E. upgrade carrier wave ring intermediate variable, use for loop control next time, so far, the control of carrier wave ring loop is accomplished;

F. adopt JPL algorithm computation envelope; Accomplish respectively the lead and lag calculating with envelope that adds up; Promptly forming the wherein said JPL algorithm of

, is the method by the calculating envelope of U.S. jet propulsion laboratory JPL proposition;

G. adopt based on the displacement and the binary division module of addition and accomplish the phase discriminator work that sign indicating number encircles, generated code ring phase demodulation error x ' (n), promptly

$\frac{1}{2}\&CenterDot;\frac{E-L}{E+L};$

H. to sign indicating number ring phase demodulation error x ' (n), sign indicating number ring intermediate variable u ' (n-1), through after suitable displacement and the add operation, realize a sign indicating number ring wave filter, generated code ring wave filter output z ' (n) encircles intermediate variable u ' (n) with new sign indicating number;

I. sign indicating number ring wave filter output z ' (n) adds that carrier wave ring wave filter output z (n) divided by the carrier wave auxiliary parameter that scale factor obtains, adds a yard IF-FRE control word, forms new code frequency control word, feeds back to track loop the sign indicating number ring is controlled;

J. upgrade sign indicating number ring intermediate variable, use for loop control next time, so far, the control of sign indicating number ring loop is accomplished.

2. the method for claim 1; It is characterized in that: in step c, the carrier wave ring wave filter is three rank filters, adopts direct II type to realize; And filter coefficient and digital controlled oscillator NCO gain taken all factors into consideration; Be approximately 2 integral number power, adopt displacement to realize, amount of displacement is according to the loop bandwidth decision of design.

3. the method for claim 1; It is characterized in that: in step h, the sign indicating number ring wave filter is a second order filter, adopts direct II type to realize; And filter coefficient and digital controlled oscillator NCO gain taken all factors into consideration; Be approximately 2 integral number power, adopt displacement to realize, amount of displacement is according to the loop bandwidth decision of design.

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