CN103414502B - Doppler frequency shift tolerance limit extended method in 2FSK spread spectrum system receiver - Google Patents

Abstract

The invention provides Doppler frequency shift tolerance limit extended method in a kind of 2FSK spread spectrum system receiver, by 2FSK Direct Sequence Spread Spectrum Signal after A/D conversion and band pass filter, be separated into two paths of signals, after respectively two paths of signals being asked modulus value respectively, calculate the difference of modulus value, again difference is sent into matched filter, there is not Doppler frequency shift in the correlation peak obtaining matched filter output, namely eliminates Doppler frequency shift.Relevant peaks due to the output of prior art matched filter is subject to the impact of Doppler frequency shift, and correlation peak is less, and main peak is widened, and side lobe levels is lifted, the relevant peaks that matched filter of the present invention exports, and compared with prior art, does not modulate f with Doppler frequency shift _d, its main peak is very narrow, is similar to impulse function, and its elsewhere secondary lobe is less, can be good at detecting relevant peaks, greatly extends Doppler frequency shift tolerance limit.

Description

Doppler frequency shift tolerance limit extended method in 2FSK spread spectrum system receiver

Technical field

The present invention relates to a kind of spectrum spread communication method, especially a kind of method of Doppler frequency shift tolerance limit expansion.

Background technology

In spread spectrum communication system, require that receiver realizes catching of pseudo-code at short notice, the value of the relevant peaks that Doppler frequency shift can cause matched filter to export reduces, thus affects catching of pseudo-code.At present, having had many scholars to be studied the expansion of Doppler frequency shift tolerance limit, but do not eliminated Doppler frequency shift, is all carried out certain expansion to Doppler frequency shift tolerance limit, and be just confined to, on phase shift keying spread-spectrum signal, not yet mention 2FSK spread-spectrum signal.In the dynamic environment of height, the Doppler frequency shift that the relative motion of transmitter and receiver causes is comparatively large, cannot relevant peaks be detected.So, be necessary to develop a kind of method eliminating 2FSK spread-spectrum signal Doppler frequency shift.

Summary of the invention

In high dynamic burst spread spectrum communication system environment, call duration time is short, Doppler frequency shift is large, traditional matched filter structure has little time to compensate Doppler frequency shift, cannot realize catching of pseudo-code, in order to overcome the deficiencies in the prior art, the special method proposing the expansion of a kind of Doppler frequency shift tolerance limit, this method can eliminate Doppler frequency shift, does not need the make-up time, significantly improves the impact of Doppler frequency shift on relevant peaks.

The technical solution adopted in the present invention is:

In 2FSK Receiver of Direct-sequence Spread Spectrum, after down-conversion, modular arithmetic is asked to I, Q two paths of signals in orthogonal double channels, eliminate Doppler frequency shift f _d, then carry out matched filtering, thus reach the object improving relevant peaks.

Concrete steps of the present invention are:

Two frequencies of step 1:2FSK Direct Sequence Spread Spectrum Signal are f ₁, f ₂, a is the baseband signal of non-modulated, and the m sequence that spread spectrum uses is PN code; 2FSK Direct Sequence Spread Spectrum Signal, after A/D conversion and band pass filter, is separated into frequency and is respectively f ₁, f ₂two paths of signals, represent the two paths of signals after separation respectively with A, B, after the Digital Down Convert of A, B two paths of signals, A road signal becomes orthogonal I, Q two paths of signals, uses I ₁₁, Q ₁₁represent, containing Doppler frequency shift f in the signal of A road _d, expression formula is:

$I_{11}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)\cos \left(2\mathrm{\πn}{T}_s{f}_d{+\mathrm{\θ}}_1\right)+n_I---\left(1\right)$

$Q_{11}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)\sin \left(2\mathrm{\πn}{T}_s{f}_d{+\mathrm{\θ}}_1\right)+n_Q---\left(2\right)$

After Digital Down Convert, B road signal becomes orthogonal I, Q two paths of signals, uses I ₂₂, Q ₂₂represent respectively, containing Doppler frequency shift f in the signal of B road _d, expression formula is:

$I_{22}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)\cos \left(2\mathrm{\πn}{T}_S{f}_d{+\mathrm{\θ}}_1\right)+n_I---\left(3\right)$

$Q_{22}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)\sin \left(2\mathrm{\πn}{T}_S{f}_d{+\mathrm{\θ}}_1\right)+n_Q---\left(4\right)$

Wherein, T _sfor the sampling interval, f _dfor Doppler frequency shift, a (nT _s) be the signal of a after A/D sampling, for a (nT _s) radix-minus-one complement, n _i, n _qfor noise, θ ₁for initial phase, PN (nT _s) be the code sequence after PN sampling, n value is 0,1,2,3,

Step 2: the modulus value A asking A road signal respectively ₁with the modulus value A of the signal on B road ₂: obtain modulus value A by formula in step 1 (1), (2) formula ₁for:

$A_1=\sqrt{I_{11}^2+Q_{11}^2}=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos ({2\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\π}{\mathrm{nT}}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2}$

(5)

Modulus value A ₂for:

$A_2=\sqrt{I_{22}^2+Q_{22}^2}=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos ({2\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\π}{\mathrm{nT}}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2}$

(6)

Wherein a (nT _s) be a (nT _s) radix-minus-one complement, order:

$n_1=\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2$

(7)

$n_2=\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2$

(8)

Step 3: calculate A ₁-A ₂, obtain:

$A_1-A_2=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_1}-\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_2}$

(9)

By A ₁-A ₂send into matched filter, obtain the correlation peak P that matched filter exports:

$P=\underset{n=1}{\overset{M}{\mathrm{\Σ}}}(\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_1{\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)}-\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_2{\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)})$

(10)

Wherein M is the tap coefficient of matched filter, PN ^/(nT _s) be PN code PN (nT _s) Inversion Sequence, from formula (10), in correlation peak P, do not occur that Doppler frequency shift is modulated, namely Doppler frequency shift is eliminated, improve relevant peaks, namely allow the tolerance limit of the Doppler frequency shift introduced to expand, reach the object of Doppler frequency shift tolerance limit expansion.

The invention has the beneficial effects as follows that the relevant peaks exported due to prior art matched filter is subject to the impact of Doppler frequency shift, correlation peak is less, and main peak is widened, side lobe levels is lifted, the relevant peaks that matched filter of the present invention exports, compared with prior art, not with Doppler frequency shift modulation f _d, its main peak is very narrow, is similar to impulse function, and its elsewhere secondary lobe is less, can be good at detecting relevant peaks, greatly extends Doppler frequency shift tolerance limit.

Accompanying drawing explanation

Fig. 1 is the structure chart of Doppler frequency shift tolerance limit expansion.

Fig. 2 is matched filter conventional junction composition, I in figure ₁₂the in-phase signal that A road matched filter exports, Q ₁₂the orthogonal signalling that A road matched filter exports, I ₂₁the in-phase signal that B road matched filter exports, Q ₂₁the orthogonal signalling that B road matched filter exports.

Fig. 3 is the relevant peaks loss that Doppler frequency shift causes.

The relevant peaks of Fig. 4 to be Doppler frequency shift be 12KHz.

Fig. 5 is that the relevant peaks of Doppler frequency shift tolerance limit expansion exports.

Embodiment

Below in conjunction with drawings and Examples, the present invention is further described.

Fig. 1 is the structure chart of Doppler frequency shift tolerance limit of the present invention expansion, and performing step of the present invention is:

Two frequencies of step 1:2FSK Direct Sequence Spread Spectrum Signal are f ₁, f ₂, a is the baseband signal of non-modulated, and the m sequence that spread spectrum uses is PN code, and this PN code is produced by ROM shift register, is realized by the IP kernel ROM called in FPGA; 2FSK Direct Sequence Spread Spectrum Signal, after A/D conversion and band pass filter, is separated into frequency and is respectively f ₁, f ₂two paths of signals, represent the two paths of signals after separation respectively with A, B, after the Digital Down Convert of A, B two paths of signals, A road signal becomes orthogonal I, Q two paths of signals, uses I ₁₁, Q ₁₁represent, containing Doppler frequency shift f in the signal of A road _d, expression formula is:

$I_{11}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)\cos \left(2\mathrm{\πn}{T}_s{f}_d{+\mathrm{\θ}}_1\right)+n_I---\left(1\right)$

$Q_{11}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)\sin \left(2\mathrm{\πn}{T}_s{f}_d{+\mathrm{\θ}}_1\right)+n_Q---\left(2\right)$

After Digital Down Convert, B road signal becomes orthogonal I, Q two paths of signals, uses I ₂₂, Q ₂₂represent respectively, containing Doppler frequency shift f in the signal of B road _d, expression formula is:

$I_{22}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)\cos \left(2\mathrm{\πn}{T}_S{f}_d{+\mathrm{\θ}}_1\right)+n_I---\left(3\right)$

$Q_{22}=\frac{1}{2}\mathrm{PN}\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)\sin \left(2\mathrm{\πn}{T}_S{f}_d{+\mathrm{\θ}}_1\right)+n_Q---\left(4\right)$

Wherein, T _sfor the sampling interval, f _dfor Doppler frequency shift, a (nT _s) be the signal of a after A/D sampling, for a (nT _s) radix-minus-one complement, n _i, n _qfor noise, θ ₁for initial phase, PN (nT _s) be the code sequence after PN sampling, n value is 0,1,2,3,

Step 2: the modulus value A asking A road signal respectively ₁with the modulus value A of the signal on B road ₂: obtain modulus value A by formula in step 1 (1), (2) formula ₁for:

$A_1=\sqrt{I_{11}^2+Q_{11}^2}=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos ({2\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\π}{\mathrm{nT}}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2}---\left(5\right)$

Modulus value A ₂for:

$A_2=\sqrt{I_{22}^2+Q_{22}^2}=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos ({2\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\π}{\mathrm{nT}}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2}---\left(6\right)$

Wherein a (nT _s) be a (nT _s) radix-minus-one complement, order:

$n_1=\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2---\left(7\right)$

$n_2=\mathrm{PN}\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)[\cos (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_I+\sin (2\mathrm{\πn}{T}_s{f}_d+{\mathrm{\θ}}_1)n_Q]+n_I^2+n_Q^2---\left(8\right)$

The present invention by using FPGA technology to realize, calls IP kernel multiplier in quartusII to realize I in quartusII environment ₁₁and Q ₁₁square, call IP kernel adder in quartusII to I ₁₁and Q ₁₁square summation;

Step 3: calculate A ₁-A ₂, obtain:

$A_1-A_2=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_1}-\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_2}---\left(9\right)$

By A ₁-A ₂send into matched filter, obtain the correlation peak P that matched filter exports:

$P=\underset{n=1}{\overset{M}{\mathrm{\Σ}}}(\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_1{\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)}-\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_2{\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)})---\left(10\right)$

Wherein M is the tap coefficient of matched filter, PN ^/(nT _s) be PN code PN (nT _s) Inversion Sequence, from formula (10), in correlation peak P, do not occur that Doppler frequency shift is modulated, namely Doppler frequency shift is eliminated, improve relevant peaks, namely allow the tolerance limit of the Doppler frequency shift introduced to expand, reach the object of Doppler frequency shift tolerance limit expansion.

Fig. 2 is the traditional structure of the matched filter in 2FSK Receiver of Direct-sequence Spread Spectrum, and the homophase that matched filter exports and quadrature branch signal are I ₁₂and Q ₁₂, ask modular arithmetic to obtain relevant peaks to it a ₁' in non-noise item be Z:

$Z=\frac{1}{2}\mathrm{NR}\left(\mathrm{\τ}\right)\left|\frac{\sin \left(\mathrm{\π}{f}_d{T}_s\right)}{\mathrm{\π}{f}_d{T}_s}\right|---\left(11\right)$

In above formula, R (τ) represents the reception pseudo-code and the correlation of local pseudo-code in a chip that postpone for τ, and N is PN code code length.From (11) formula, the relevant peaks of the matched filter output of traditional structure is subject to the modulation of Doppler frequency shift.This modulation causes the loss item of relevant peaks can represent with attenuation coefficient η:

$\mathrm{\η}=20{\log }_{10}\left|\frac{\sin \left(\mathrm{\π}{f}_d{T}_s\right)}{\mathrm{\π}{f}_d{T}_s}\right|---\left(12\right)$

Fig. 3 is the relevant peaks loss that Doppler frequency shift causes, and in figure, ordinate represents attenuation coefficient, abscissa f _d, T _sbe 40 μ s.

The present embodiment adopts 8 grades of shift registers to produce the maximum length m sequence of 255, and the amplitude of signal is 1V, and the signal to noise ratio in signal bandwidth is-10dB.Traditional matched filter is at Doppler frequency shift f _dduring=12KHz, export as Fig. 4.The output of modified node method matched filter in this paper is as Fig. 5.

As can be seen from Figure 4, traditional structure is at f _dduring=12KHz, this Doppler modulation frequency, decreases correlation peak, and sidelobe structure is changed, and can not detect relevant peaks.And the method utilizing the process structure shown in Fig. 1 and the present invention to propose can extend Doppler frequency shift tolerance limit greatly, in Fig. 5, its relevant peaks main peak is very narrow, is similar to impulse function, can be good at detecting relevant peaks, demonstrates the validity of the method.

PN described in step 3 of the present invention ^/(nT _s) be used for carrying out despreading to 2FSK Direct Sequence Spread Spectrum Signal, from formula (10), do not occur that Doppler frequency shift is modulated in correlation P, namely eliminate Doppler frequency shift, improve relevant peaks.The process structure of conventional matched-filter only allows the 2FSK Direct Sequence Spread Spectrum Signal received to introduce the Doppler frequency shift of certain limit, and values of Doppler frequency shift is the smaller the better, exceeds the scope that 2FSK spread spectrum system receiver specifies, cannot obtain correlation peak.Even and if the 2FSK Direct Sequence Spread Spectrum Signal that the processing method receiver that the present invention proposes receives introduces very large Doppler frequency shift, through formula (5), (6), (7), (8), (9), the computing of (10) formula, eliminate Doppler frequency shift the most at last, in relevant peaks, will not Doppler frequency shift f be contained _dthat is, the scope of the Doppler frequency shift that the 2FSK Direct Sequence Spread Spectrum Signal that processing method of the present invention allows receiver to receive is introduced is very large, namely allows the tolerance limit of the Doppler frequency shift introduced to expand, so reach the object of Doppler frequency shift tolerance limit expansion.

Traditional processing method is I ₁₁, Q ₁₁, I ₂₂, Q ₂₂direct feeding matched filter, then to the I that matched filter exports ₁₂, Q ₁₂, I ₂₁, Q ₂₁carry out the realization of quadratic sum.And the present invention is I ₁₁, Q ₁₁, I ₂₂, Q ₂₂first through formula (5), the process of (6) and (9), then send matched filter to, by this process, achieve the expansion of doppler tolerance, be also the difference with conventional method.

Claims (1)

1. a Doppler frequency shift tolerance limit extended method in 2FSK spread spectrum system receiver, is characterized in that comprising the steps:

Two frequencies of step 1:2FSK Direct Sequence Spread Spectrum Signal are f ₁, f ₂, a is the baseband signal of non-modulated, and the m sequence that spread spectrum uses is PN code; 2FSK Direct Sequence Spread Spectrum Signal, after A/D conversion and band pass filter, is separated into frequency and is respectively f ₁, f ₂two paths of signals, represent the two paths of signals after separation respectively with A, B, after the Digital Down Convert of A, B two paths of signals, A road signal becomes orthogonal I, Q two paths of signals, uses I ₁₁, Q ₁₁represent, containing Doppler frequency shift f in the signal of A road _d, expression formula is:

$I_{11}=\frac{1}{2}PN\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)cos(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)+n_I---\left(1\right)$

$Q_{11}=\frac{1}{2}PN\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)sin(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)+n_Q---\left(2\right)$

After Digital Down Convert, B road signal becomes orthogonal I, Q two paths of signals, uses I ₂₂, Q ₂₂represent respectively, containing Doppler frequency shift f in the signal of B road _d, expression formula is:

$I_{22}=\frac{1}{2}PN\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)cos(2{\mathrm{\πnT}}_S{f}_d+{\mathrm{\θ}}_1)+n_I---\left(3\right)$

$Q_{22}=\frac{1}{2}PN\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)sin(2{\mathrm{\πnT}}_S{f}_d+{\mathrm{\θ}}_1)+n_Q---\left(4\right)$

Wherein, T _sfor the sampling interval, f _dfor Doppler frequency shift, a (nT _s) be the signal of a after A/D sampling, for a (nT _s) radix-minus-one complement, n _i, n _qfor noise, θ ₁for initial phase, PN (nT _s) be the code sequence after PN sampling, n value is 0,1,2,3,

Step 2: the modulus value A asking A road signal respectively ₁with the modulus value A of the signal on B road ₂: obtain modulus value A by formula in step 1 (1), (2) formula ₁for:

$A_1=\sqrt{I_{11}^2+Q_{11}^2}=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+PN\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)\[\cos \left(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1\right)n_I+\sin \left(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1\right)n_Q\]+n_I^2+n_Q^2}---\left(5\right)$

Modulus value A ₂for:

$A_2=\sqrt{I_{22}^2+Q_{22}^2}=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\tilde{a}}^2\left({\mathrm{nT}}_s\right)+PN\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)\[\cos \left(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1\right)n_I+\sin \left(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1\right)n_Q\]+n_I^2+n_Q^2}---\left(6\right)$

Wherein for a (nT _s) radix-minus-one complement, order:

$n_1=PN\left({\mathrm{nT}}_s\right)a\left({\mathrm{nT}}_s\right)\[cos(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_I+sin(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_Q\]+n_I^2+n_Q^2---\left(7\right)$

$n_2=PN\left({\mathrm{nT}}_s\right)\tilde{a}\left({\mathrm{nT}}_s\right)\[cos(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_I+sin(2{\mathrm{\πnT}}_s{f}_d+{\mathrm{\θ}}_1)n_Q\]+n_I^2+n_Q^2---\left(8\right)$

Step 3: calculate A ₁-A ₂, obtain:

$A_1-A_2=\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_1}-\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\tilde{a}}^2\left({\mathrm{nT}}_s\right)+n_2}---\left(9\right)$

By A ₁-A ₂send into matched filter, obtain the correlation peak P that matched filter exports:

$P=\underset{n=1}{\overset{M}{\Σ}}(\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)a^2\left({\mathrm{nT}}_s\right)+n_1{\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)}-\sqrt{\frac{1}{4}{\mathrm{PN}}^2\left({\mathrm{nT}}_s\right){\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right){\tilde{a}}^2\left({\mathrm{nT}}_s\right)+n_2{\mathrm{PN}}^{/2}\left({\mathrm{nT}}_s\right)})---\left(10\right)$

Wherein M is the tap coefficient of matched filter, PN ^/(nT _s) be PN code PN (nT _s) Inversion Sequence, from formula (10), in correlation peak P, do not occur that Doppler frequency shift is modulated, namely Doppler frequency shift is eliminated, improve relevant peaks, namely allow the tolerance limit of the Doppler frequency shift introduced to expand, reach the object of Doppler frequency shift tolerance limit expansion.