CN104865558A - Combined optimization method for phase-coded signal and mismatched filter based on p-norm - Google Patents

Abstract

The invention belongs to the technical field of radar, and discloses a combined optimization method for phase-coded signals and a mismatched filter based on a p-norm. The combined optimization method comprises the following steps: setting code element length of a phase-coded signal and length of a mismatched filter, and maximum signal to noise ratio loss; determining a mismatched filter output result of the phase-coded signal which passes through the mismatched filter, and peak-sidelobe level of the mismatched filter output result of the phase-coded signal which passes through the mismatched filter; establishing an optimization standard of the phase-coded signal and the mismatched filter; performing formal transformation on the optimization standard; solving to obtain phase of the phase-coded signal, phase of the mismatched filter, and amplitude of the mismatched filter; and establishing the phase-coded signal and the mismatched filter. The method can reduce distance sidelobe level of a radar reception channel.

Description

Based on the phase-coded signal of p norm and the combined optimization method of mismatched filter

Technical field

The invention belongs to Radar Technology field, be specifically related to a kind of based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, for reducing the distance side lobe level of radar receiving cable.

Background technology

Pulse compression technique solves the contradiction between the operating distance of radar and range resolution, but pulse compression signal has higher distance side lobe usually, and higher distance side lobe is unfavorable for that radar effectively detects target, Faint target detection particularly under multiple goal or strong clutter background, the main lobe of weak signal target is very easily flooded by the distance side lobe of strong target echo and causes false dismissal.Therefore the signal waveform with distance good sidelobe performance is designed significant to the detection performance improving radar.

From domestic and international to phase-coded signal research conditions at present, two kinds are suppressed the method for distance side lobe to be encode preferably and mismatch filter respectively.The method in the past obtaining low distance side lobe signal is the coded signal adopting certain class special, and the major way obtaining phase-coded signal modern age is then solved by optimized algorithm.The sidelobe level that can be reached by the method optimizing phase-coded signal autocorrelation sidelobe is usually still higher.

Therefore the method for mismatch filter can be adopted to reduce the sidelobe level of system further at receiving end.Phase-coded signal is constant modulus signals normally, and the weight coefficient of mismatched filter then can break through this restriction, realizes lower distance side lobe and exports.Due to the problem of optimization means, phase-coded signal and mismatched filter are optimized by mismatch filter algorithm in the past usually respectively, and the mode optimized by intersection is solved problem, and the distance side lobe that this algorithm can reduce system effectively exports.

Existing method is by optimizing a collection of low distance side lobe phase-coded signal and is search starting point based on these signals, finds the weight coefficient of phase-coded signal and mismatched filter simultaneously.But if the start signal of phase-coded signal is the phase-coded signal with low distance side lobe level, then existing method may get rid of the optimum results that some may be more excellent.

Summary of the invention

For above-mentioned technical matters, the object of the present invention is to provide a kind of based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, the distance side lobe level after phase-coded signal pulse compression can be reduced.

Realizing technical thought of the present invention is: produce its initial value at random according to the Baud Length of phase-coded signal and the length of mismatched filter, under maximum signal to noise ratio loss is the condition of constraint, to minimize the peak sidelobe after mismatch filter for Optimality Criteria, combined optimization designed phase coded signal and mismatched filter, and use the Least p-norm optimized algorithm based on L-BFGS (limited memory Broyden-Fletcher-Goldfarb-Shanno, Quasi-Newton algorithm) to solve.

For achieving the above object, the present invention adopts following technical scheme to be achieved.

The embodiment of the present invention provides a kind of based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, it is characterized in that, comprises the following steps:

Step 1, the Baud Length N of setting phase-coded signal s _swith the length N of mismatched filter h _h, and maximum signal to noise ratio loss SNR _loss, wherein, N _h>=N _sand N _h+ N _sfor even number;

Step 2, determines the mismatched filter Output rusults of described phase-coded signal s by described mismatched filter h and described phase-coded signal s is by the peak sidelobe of the mismatched filter Output rusults ρ of described mismatched filter h wherein, represent convolution, [.] ^trepresent transposition, and i ∈ [1,2 ..., N _s+ N _h-1];

Step 3, by described maximum signal to noise ratio loss SNR _lossas constraint condition, to minimize described peak sidelobe PSL for objective function, the Optimality Criteria building described phase-coded signal s and described mismatched filter h is

Wherein, energy differences γ and peak difference values δ presets, for the phase place of described phase-coded signal s, θ is the phase place of described mismatched filter h, and A is the amplitude of described mismatched filter h;

Step 4, carries out formal transformation to described Optimality Criteria, obtains

$\underset{x}{\min }{\left|\right|{\mathrm{\ρ}}_s\left|\right|}_{\∞}+\mathrm{\α}\·|h^{H}h-s^{H}s|+\mathrm{\β}\·|{\mathrm{\ρ}}_{(N_h+N_s)/2}-N_s|,$

Wherein, vector x is the phase place of described phase-coded signal s , the amplitude A of described mismatched filter h and described mismatched filter h the column vector of phase theta composition wherein, ρ _sfor by the result of described phase-coded signal s through the sidelobe level delivery value of the mismatched filter Output rusults ρ of described mismatched filter h, the value of energy weight coefficient α and peak value weight coefficient β belongs in the scope of [0,1];

Step 5, solves $\underset{x}{\min }{\left|\right|{\mathrm{\ρ}}_s\left|\right|}_{\∞}+\mathrm{\α}\·|h^{H}h-s^{H}s|+\mathrm{\β}\·|{\mathrm{\ρ}}_{(N_h+N_s)/2}-N_s|,$ Obtain described vector x, thus obtain the phase place of described phase-coded signal s the amplitude A of described mismatched filter h and the phase theta of described mismatched filter h;

Step 6, according to the phase place of described phase-coded signal s construct described phase-coded signal according to the phase theta of described mismatched filter h and the amplitude A of described mismatched filter h, construct described mismatched filter h=A ⊙ exp (j θ).

The feature of technical solution of the present invention and being further improved to:

The γ of energy differences described in step 3 according to determine, described peak difference values δ according to determine, wherein, SNR _lossfor maximum signal to noise ratio loss, N _sfor the Baud Length of described phase-coded signal s.

The optimized algorithm of the Least p-norm based on L-BFGS is adopted to solve in step 5

$\underset{x}{\min }{\left|\right|{\mathrm{\ρ}}_s\left|\right|}_{\∞}+\mathrm{\α}\·|h^{H}h-s^{H}s|+\mathrm{\β}\·|{\mathrm{\ρ}}_{(N_h+N_s)/2}-N_s|,$ Obtain described vector x.

Further, the optimized algorithm of the Least p-norm based on L-BFGS is adopted to solve

$\underset{x}{\min }{\left|\right|{\mathrm{\ρ}}_s\left|\right|}_{\∞}+\mathrm{\α}\·|h^{H}h-s^{H}s|+\mathrm{\β}\·|{\mathrm{\ρ}}_{(N_h+N_s)/2}-N_s|,$ Obtain described vector x, specifically comprise following sub-step:

(5a) defined function $f\left(x\right)={\left|\right|{\mathrm{\ρ}}_s\left|\right|}_p+\mathrm{\α}\·|h^{H}h-s^{H}s|+\mathrm{\β}\·|{\mathrm{\ρ}}_{(N_h+N_s)/2}-N_s|;$

(5b) the initial value x of described vector x is set ₀, minimum descent ε ₁initial value and the initial value of iterations n be 1, the initial value p of norm p ₀, the value of multiplier μ and the initial value f of described function f (x) ₀;

(5c) vector x is used _n-1as initial value, by minimization function f (x _n-1) try to achieve optimum results vector x _n, make f _n=f (x _n);

If (5d) | f _n-f _n-1| < ε ₁, then output vector x _n, and stop circulation; Otherwise iterations n adds 1, and makes norm p _n=μ p _n-1, and skip to sub-step (5c) continuation execution;

(5e) described vector x is determined.

The present invention compared with prior art tool has the following advantages.Technical solution of the present invention is under the loss of certain letter ratio is the condition of constraint, to minimize the peak sidelobe after mismatch filter for criterion, combined optimization designed phase coded signal and mismatched filter, and use the Least p-norm optimized algorithm based on L-BFGS to solve, the peak sidelobe after phase-coded signal mismatch filter can be reduced further.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.

Fig. 1 is the schematic flow sheet based on the phase-coded signal of p norm and the combined optimization method of mismatched filter that the embodiment of the present invention provides;

Fig. 2 is the schematic flow sheet of the Least p-norm optimized algorithm based on L-BFGS that the embodiment of the present invention provides;

Fig. 3 is the schematic diagram of the normalized peak sidelobe that matched filter exports, and horizontal ordinate represents relative time delay, and unit is us, and ordinate represents amplitude, and unit is dB;

Fig. 4 is with document [Nunn C.Constrained optimization applied to pulsecompression codes and filters [C] .IEEE International Radar Conference, 2005:190-194.] method mismatch filter after the normalized peak sidelobe figure that exports, horizontal ordinate represents relative time delay, unit is us, ordinate represents amplitude, and unit is dB;

Fig. 5 is the normalized peak sidelobe figure of the mismatched filter output that the embodiment of the present invention provides, and horizontal ordinate represents relative time delay, and unit is us, and ordinate represents amplitude, and unit is dB;

Fig. 6 is the normalized peak sidelobe figure of Fig. 5 initial phase coded signal, and horizontal ordinate represents relative time delay, and unit is us, and ordinate represents amplitude, and unit is dB.

Embodiment

As shown in Figure 1, the embodiment of the present invention provide based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, comprise the steps:

Step 1, the Baud Length N of setting phase-coded signal s _swith the length N of mismatched filter h _h, and maximum signal to noise ratio loss SNR _loss.

Wherein, N _h>=N _s, and N _h+ N _sfor even number.Normal conditions require snr loss SNR _loss≤ 1dB.

Step 2, determines the mismatched filter Output rusults of phase-coded signal s by mismatched filter h and phase-coded signal s is by the peak sidelobe of the mismatched filter Output rusults ρ of mismatched filter h $\mathrm{PSL}=\underset{k\&NotEqual;(N_h+N_s)/2}{\max }\left(\right|{\mathrm{\&rho;}}_k\left|\right)/\left|{\mathrm{\&rho;}}_{k=(N_h+N_s)/2}\right|.$

Wherein, represent convolution, [.] ^trepresent transposition, and i ∈ [1,2 ..., N _s+ N _h-1].

Suppose that phase-coded signal is s, mismatched filter is that h, phase-coded signal s are expressed as by the mismatched filter Output rusults ρ of mismatched filter h:

$p=s\&CircleTimes;h={[{\mathrm{\&rho;}}_1,{\mathrm{\&rho;}}_2,...,{\mathrm{\&rho;}}_i,...,{\mathrm{\&rho;}}_{N_s+N_h-1}]}^T$

Wherein, represent convolution, [.] ^trepresent transposition, and i ∈ [1,2 ..., N _s+ N _h-1], N _srepresent the Baud Length of phase-coded signal s, N _hrepresent the length of mismatched filter h.

Phase-coded signal s by the peak sidelobe of the mismatched filter Output rusults ρ of mismatched filter h is:

$\mathrm{PSL}=\underset{k\&NotEqual;(N_h+N_s)/2}{\max }\left(\right|{\mathrm{\&rho;}}_k\left|\right)/\left|{\mathrm{\&rho;}}_{k=(N_h+N_s)/2}\right|.$

Wherein, || represent delivery value, k ∈ [1, N _s+ N _h-1].

Step 3, loses SNR by maximum signal to noise ratio _lossas constraint condition, to minimize peak sidelobe

PSL is objective function, and the Optimality Criteria building phase-coded signal s and mismatched filter h is

Wherein, energy differences γ and peak difference values δ presets, for the phase place of phase-coded signal s, θ is the phase place of mismatched filter h, and A is the amplitude of mismatched filter h.

In the loss of given maximum signal to noise ratio under constraint condition, to minimize the peak sidelobe after mismatch filter for objective function, the Optimality Criteria building phase-coded signal s and mismatched filter h is as follows:

Wherein, PSL is the peak sidelobe that mismatched filter exports, for the phase vectors of phase-coded signal s, namely a and θ is respectively amplitude and the phase place of mismatched filter h, i.e. h=A ⊙ exp (j θ), ⊙ represents dot product, exp () represents exponential function, j is imaginary unit, energy differences γ and peak difference values δ is that energy differences γ and peak difference values δ can determine according to following experimental formula respectively artificially according to the arithmetic number of maximum signal to noise ratio loss setting

Here the energy differences γ determined and peak difference values δ is an experimental formula, in practice, the simulation result obtained according to this experimental formula may depart from the snr loss of actual requirement, now need artificially to adjust the value of energy differences γ and peak difference values δ, the process of the value adjustment of energy differences γ and peak difference values δ follows following rule: when energy differences γ immobilizes, peak difference values δ is larger, and snr loss is larger, but peak sidelobe now can reduce; When peak difference values δ immobilizes, energy differences γ is larger, and snr loss is less, but peak sidelobe now can raise.Therefore, compromise is needed to consider when determining energy differences γ and peak difference values δ.

Step 4, carries out formal transformation to the Optimality Criteria of phase-coded signal s and mismatched filter h, obtains $\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|,$

Wherein, vector x is by the phase place of phase-coded signal s , the amplitude A of mismatched filter h and mismatched filter h the column vector of phase theta composition ${\mathrm{\&rho;}}_s={\left[\right|{\mathrm{\&rho;}}_1|,|{\mathrm{\&rho;}}_2|,...,|{\mathrm{\&rho;}}_i|,...,|{\mathrm{\&rho;}}_{N_s+N_h-1}\left|\right]}^T,$ ρ _sfor by the result of phase-coded signal s through the sidelobe level delivery value of the mismatched filter Output rusults ρ of mismatched filter h, the value of energy weight coefficient α and peak value weight coefficient β belongs in the scope of [0,1].

In order to solve conveniently, changed by the Optimality Criteria of phase-coded signal s and mismatched filter h, it specifically comprises following sub-step:

(4a) phase-coded signal s is designated as through the result of the sidelobe level delivery value of the mismatched filter Output rusults ρ of mismatched filter h:

${\mathrm{\&rho;}}_s={\left[\right|{\mathrm{\&rho;}}_1|,|{\mathrm{\&rho;}}_2|,...,|{\mathrm{\&rho;}}_i|,...,|{\mathrm{\&rho;}}_{N_s+N_h-1}\left|\right]}^T,$

Wherein, and i ∈ [1,2 ..., N _s+ N _h, and i ≠ (N-1] _h+ N _s)/2, N _srepresent the Baud Length of phase-coded signal s, N _hrepresent the length of mismatched filter h.

(4b) Optimality Criteria after conversion is:

$\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|$

Wherein, vector x is by the phase place of phase-coded signal s the column vector of the amplitude A of mismatched filter h and the phase theta composition of mismatched filter h || || _∞represent Infinite Norm, energy weight coefficient α and peak value weight coefficient β is the arithmetic number of artificial setting, for the size of compromise Sidelobe Suppression effect and snr loss, the value of energy weight coefficient α and peak value weight coefficient β is respectively [0,1] select in scope, then adjust according to the snr loss in actual emulation result.

Objective function peak sidelobe PSL can be written as || ρ _s|| _∞.In fact, minimize || ρ _s|| _∞can by minimizing || ρ _s|| _prealize, along with the increase of p numerical value, minimize a series of || ρ _s|| _pcan approximately equivalent for minimizing || ρ _s|| _∞, wherein, || || _∞represent Infinite Norm, || || _prepresent p norm, p>=2.

For the Solve problems of above-mentioned Optimality Criteria, existing Minimax Algorithm can be used to be optimized and to solve; The embodiment of the present invention uses a kind of minimax optimized algorithm based on Least p-norm to solve.

Step 5, solves $\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|,$ Obtain vector x, thus obtain the phase place of phase-coded signal s the phase theta of mismatched filter h and the amplitude A of mismatched filter h.

As shown in Figure 2, for adopting the optimized algorithm based on the Least p-norm of L-BFGS to solve $\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|,$ Obtain the concrete sub-step of vector x, comprising:

(5a) defined function: $f\left(x\right)={\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_p+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|;$

(5b) the initial value x of vector x is set ₀with minimum descent ε ₁initial value, and the initial value of iterations n is the initial value p of 1, norm p ₀, multiplier μ=2, function initial value f ₀=100;

(5c) by using document [Wang Y C, Wang X, Liu H W, et al.On the Design ofConstant Modulus Probing Signals for MIMO Radar Signal Processing [J] .IEEETransactions on Signal Processing, 2012,60 (8): 4432-4438.] L-BFGS algorithmic minimizing function f (x), wherein, the update times m=5 of L-BFGS algorithm, vector x _n-1as the initial value of L-BFGS algorithm, optimum results is vector x _n, make f _n=f (x _n);

If (5d) | f _n-f _n-1| < ε ₁, then output vector x _nand stop circulation; Otherwise iterations n adds 1, and makes norm p _n=μ p _n-1, skip to sub-step (5c);

(5e) vector x obtained by above-mentioned sub-step _n, determine vector thus determine the phase place of phase-coded signal s the phase theta of mismatched filter h and the amplitude A of mismatched filter h.

Step 6, according to the phase place of phase-coded signal s construct described phase-coded signal according to the phase theta of mismatched filter h and the amplitude A of mismatched filter h, structure mismatched filter h=A ⊙ exp (j θ).

The vector x obtained after being optimized by step 5, thus the phase place of phase-coded signal s by the 1st in column vector x to N _sindividual element composition, the amplitude A of mismatched filter h is by the N in column vector x _s+ 1 to N _s+ N _hindividual element composition, the phase theta of mismatched filter h is by the N in column vector x _s+ N _h+ 1 to N _s+ N _h+ N _hindividual element composition, then phase-coded signal mismatched filter h=A ⊙ exp (j θ), wherein ⊙ represents dot product.

Effect of the present invention can be further illustrated by following simulation result:

(1) simulated conditions

The he number N of phase-coded signal in this emulation _s=128, the length N of mismatched filter _h=256, snr loss SNR _loss≤ 0.25dB.

(2) content is emulated

Emulation 1, utilizes Least p-norm algorithm optimization Baud Length to be the phase-coded signal of 128, and the phase place initial value of phase-coded signal is random generation, and Fig. 3 is the matched filtering result of signal.As shown in Figure 3, the peak sidelobe after matched filtering is-35.9332dB.

Emulation 2, signal after utilizing emulation 1 to optimize and document [Nunn C.Constrained optimizationapplied to pulse compression codes and filters [C] .IEEE International RadarConference, 2005:190-194.] in weighted iteration least square method design mismatched filter, Fig. 4 is the result after mismatch filter.After mismatch filter, peak sidelobe is-42.1827dB as shown in Figure 4, and snr loss is-0.2448dB.

Emulation 3, simulated conditions weights α=0.2, β=0.35, for each optimal design, the phase place of phase-coded signal s , the amplitude A of mismatched filter h and the initial value of phase theta be all random generation, optimizes the result choosing optimum for 100 times, Fig. 5 is the mismatched filter Output rusults after phase-coded signal s and mismatched filter h combined optimization.As shown in Figure 5, peak sidelobe is-45.5728dB, and snr loss is-0.1903dB.

Fig. 6 is the normalized peak sidelobe figure of Fig. 5 initial phase coded signal, compared with the result of Fig. 3, and peak sidelobe in Fig. 6 is high 20.0641dB; Compared with the result in Fig. 4, the peak sidelobe in Fig. 5 reduces 3.3901dB, and snr loss is less.Therefore, by combined optimization phase-coded signal s and mismatched filter h, start-phase coded signal is without the need to there being lower sidelobe level; And under the condition that snr loss is certain, the peak sidelobe after mismatch filter can be reduced further.

More than describing is only example of the present invention, does not form any limitation of the invention.Obviously for those skilled in the art; after having understood content of the present invention and principle; all may when not deviating from the principle of the invention, structure; carry out the various correction in form and details and change, but these corrections based on inventive concept and change are still within claims of the present invention.

Claims (4)

1., based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, it is characterized in that, comprise the following steps:

Step 1, the Baud Length N of setting phase-coded signal s _swith the length N of mismatched filter h _h, and maximum signal to noise ratio loss SNR _loss, wherein, N _h>=N _sand N _h+ N _sfor even number;

Step 2, determines the mismatched filter Output rusults of described phase-coded signal s by described mismatched filter h and described phase-coded signal s is by the peak sidelobe of the mismatched filter Output rusults ρ of described mismatched filter h wherein, represent convolution, [.] ^trepresent transposition, and i ∈ [1,2 ..., N _s+ N _h-1];

Step 3, by described maximum signal to noise ratio loss SNR _lossas constraint condition, to minimize described peak sidelobe PSL for objective function, the Optimality Criteria building described phase-coded signal s and described mismatched filter h is

s.t. |h ^Hh-s ^Hs|≤γ

$|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|\&le;\mathrm{\&delta;}$

Wherein, energy differences γ and peak difference values δ presets, for the phase place of described phase-coded signal s, θ is the phase place of described mismatched filter h, and A is the amplitude of described mismatched filter h;

Step 4, formal transformation is carried out to described Optimality Criteria, obtains:

$\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|$

Wherein, vector x is the phase place of described phase-coded signal s the column vector of the amplitude A of described mismatched filter h and the phase theta composition of described mismatched filter h wherein, ρ _sfor by the result of described phase-coded signal s through the sidelobe level delivery value of the mismatched filter Output rusults ρ of described mismatched filter h, the value of energy weight coefficient α and peak value weight coefficient β belongs in the scope of [0,1];

Step 5, solves $\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|,$ Obtain described vector x, thus obtain the phase place of the phase-coded signal s after combined optimization the amplitude A of mismatched filter h and the phase theta of mismatched filter h;

Step 6, according to the phase place of the phase-coded signal s after combined optimization construct described phase-coded signal according to the phase theta of described mismatched filter h and the amplitude A of described mismatched filter h, construct described mismatched filter

2. as claimed in claim 1 based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, it is characterized in that, the γ of energy differences described in step 3 according to determine, described peak difference values δ according to determine, wherein, SNR _lossfor maximum signal to noise ratio loss, N _sfor the Baud Length of described phase-coded signal s.

3. as claimed in claim 1 based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, it is characterized in that, adopt the optimized algorithm of the Least p-norm based on L-BFGS to solve in steps of 5 $\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|,$ Obtain described vector x.

4. as claimed in claim 3 based on the phase-coded signal of p norm and the combined optimization method of mismatched filter, it is characterized in that, adopt the optimized algorithm of the Least p-norm based on L-BFGS to solve $\underset{x}{\min }{\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_{\&infin;}+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|,$ Obtain described vector x, specifically comprise following sub-step:

(5a) defined function $f\left(x\right)={\left|\right|{\mathrm{\&rho;}}_s\left|\right|}_p+\mathrm{\&alpha;}\&CenterDot;|h^{H}h-s^{H}s|+\mathrm{\&beta;}\&CenterDot;|{\mathrm{\&rho;}}_{(N_h+N_s)/2}-N_s|;$

(5b) the initial value x of described vector x is set ₀, minimum descent ε ₁initial value and the value of iterations n, the initial value p of norm p ₀, the value of multiplier μ and the initial value f of described function f (x) ₀;

(5c) vector x is used _n-1as initial value, by minimization function f (x _n-1) try to achieve optimum results vector x _n, make f _n=f (x _n);

If (5d) | f _n-f _n-1| < ε ₁, then output vector x _n, and stop circulation; Otherwise iterations n adds 1, and makes norm p _n=μ p _n-1, and and skip to sub-step (5c) continue perform;

(5e) described vector x is determined.