CN104753561A  Direct sequence spread spectrum modulation method for suppressing multipath interference in underwater acoustic communication  Google Patents
Direct sequence spread spectrum modulation method for suppressing multipath interference in underwater acoustic communication Download PDFInfo
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 CN104753561A CN104753561A CN201310739788.3A CN201310739788A CN104753561A CN 104753561 A CN104753561 A CN 104753561A CN 201310739788 A CN201310739788 A CN 201310739788A CN 104753561 A CN104753561 A CN 104753561A
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Abstract
The invention provides a direct sequence spread spectrum modulation method for suppressing multipath interference in underwater acoustic communication. According to the direct sequence spread spectrum modulation method, a complementary sequence pair is introduced to underwater acoustic communication as a pseudorandom sequence of direct sequence spread spectrum modulation, better multipath suppression capability than that of an ordinary finitelength random sequence is achieved by using an ideal correlation function constructed in a zero correlation window, and multipath interference in underwater acoustic spread spectrum communication can be suppressed completely. According to the actual need, a pseudorandom sequence of direct sequence spread spectrum modulation can be constructed by combining two types of 'complementary sequence' pairs. By adopting a timedivision orthogonal combination mode, the emission duty ratio can be reduced, and an effect of power amplifier cooling can be achieved. A signal is not sensitive to carrier phase when demodulated in an orthogonal mode, and no precise carrier phase synchronization is needed. The efficiency of information transmission by a carrier phase orthogonal combination mode is consistent with spread spectrum modulation of ordinary m sequences, Gold sequences and other pseudorandom sequences. The method has high demodulation bit error rate at high signaltonoise ratio.
Description
Technical field
The invention belongs to underwater sound spreadspectrum communication technical field, particularly relate to a kind of direct sequence spread spectrum modulator approach suppressing Multipath interference in underwater sound communication.
Background technology
In underwater sound communication, the intersymbol interference (ISI) that multipath effect causes is the main cause of restricted information transmission rate.To this, modulate by utilizing direct sequence spread spectrum and can not only improve the transmission range of signal, also can according to the sharppointed autocorrelation performance of PRN code, multipath signals time delay being greater than to a spreadspectrum code chip has very strong inhibitory action.Therefore, receive based on the underwater sound communication of DSSS modulation system and study widely.In DSSS modulation technique, conventional spreading code has m sequence, Gold code, Constructing Chaotic Code etc.But in engineering uses, the spreading code of finite length can only be used for the modulation and demodulation of signal.But, known by Welch circle provided in document " Welch L R.Lower bounds on the maximumcrosscorrelation of signals [J] .IEEE Transactions Information Theory; 1974; 20:397399. ", for the random sequence of limited length, desirable autocorrelation or crosscorrelation function can not be obtained.Therefore, nonideal autocorrelation and crosscorrelation make spread spectrum system can not suppress intersymbol interference (ISI) and multiaccess inference (MAI) completely, improve the correlation properties of random sequence, become one of effective means suppressing Multipath interference.
In order to reduce even to eliminate intersymbol interference (ISI) and multiaccess inference (MAI), the LS code for LASCDMA system is given in document " Sta ' nczak S.BocheH.Haardt M.Are LAScodes a miracle [J] .Global Telecommunications Conference; 2001.GLOBECOM'01.IEEE; 2001,1:589593. ".This LS code is that one has zero correlation window (IFW) " complementary series " (Complementary Series), and in zero correlation window, " complementary series " is to having desirable autocorrelation and crosscorrelation function.The proposition of this spreading code, is mainly used in mobile radio communication network, in order to reduce intersymbol interference (ISI) and the multiaccess inference (MAI) of cdma system, improves the capacity of cellular network.
Summary of the invention
The object of the invention is to, the technical problem of Multipath interference in underwater sound communication can not be suppressed completely for solving existing direct sequence spread spectrum modulator approach, a kind of direct sequence spread spectrum modulator approach suppressing Multipath interference in underwater sound communication is provided, this direct sequence spread spectrum modulator approach using complementary series to the pseudo random sequence of modulating as direct sequence spread spectrum, introduce underwater sound communication, ideal correlation function in the zero correlation window utilizing it to construct, realizes having better many ways rejection ability than common limited long random sequence.
To achieve these goals, the invention provides a kind of direct sequence spread spectrum modulator approach suppressing Multipath interference in underwater sound communication, this direct sequence spread spectrum modulator approach comprises:
Step 1) constructs two and meets " complementary series " to the sequence of relation;
Step 2) two sequences obtained in step 1) are carried out Orthogonal Composite generation pseudo random sequence, using this pseudo random sequence as spreading code;
Step 3), according to the transmission bandwidth of spreadspectrum signal, calculates the duration of single spreading code chip, according to the rate of information throughput, calculates the duration of single information chip, then calculates the chip number of the spreading code corresponding to single information chip;
Step 4) according to the result calculated in step 3), by the information chip launched according to corresponding number relation respectively with step 2) in after the pseudo random sequence that obtains does mould 2 multiplication operation, combination producing complex base band spreadspectrum signal;
The complex base band spreadspectrum signal obtained in step 4) is multiplied with signal carrier and gets real part by step 5), obtains spread spectrum transmission signal.
As the further improvement of technique scheme, each sequence generated in step 1) is expressed as on continuoustime domain:
Wherein, the length of sequence is that N, t represent the time, c
_{n}represent the sequential value of the nth pseudo random sequence, rect () is square wave function
t
_{c}represent the duration of the single chip of pseudo random sequence;
The correlation function that described " complementary series " is right is defined as:
Wherein, τ represents sequence A
_{i}and A
_{j}time delay, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance; I ≠ j then describes their cross correlation.
As the further improvement of technique scheme, the information chip launched in described step 4) is expressed as:
Wherein, d
_{n}represent the nth information sequence value, t represents the time, T
_{d}represent the time that single information sequence continues.
As the further improvement of technique scheme, the signal carrier in described step 5) is expressed as:
Wherein,
represent imaginary unit, ω is carrier angular frequencies,
for carrier wave initial phase, t represents the time.
As the further improvement of technique scheme, described step 2) middle Orthogonal Composite generation pseudo random sequence employing time division way, after being arranged by two sequences sequencing temporally, the value adding certain length between two sequences is the sequence of 0, and the pseudo random sequence obtained is expressed as:
Wherein, A
_{n}and B
_{n}represent sequence, W represents the number of add between two sequences 0, and S represents pseudo random sequence, and its length is 2 (N+W);
According to the definition of correlation function, the correlation function of formula (5) is expressed as:
Wherein, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance; I ≠ j then describes their cross correlation.
As the further improvement of technique scheme, obtaining spread spectrum transmission signal indication in described step 5) is:
Wherein, T
_{c}represent the duration of the single chip of pseudo random sequence, t represents the time,
expression information chip,
with
represent sequence, ω is carrier angular frequencies
for carrier wave initial phase, T
_{d}represent the time that single information sequence continues.
As the further improvement of technique scheme, described step 2) middle Orthogonal Composite generation pseudo random sequence employing carrier phase orthogonal manner, two sequences be adjusted to respectively on the quadrature carrier that phase is 90 degree, the pseudo random sequence obtained is expressed as:
CS＝A
_{n}+jB
_{n}（8）
Wherein, A
_{n}and B
_{n}represent sequence,
represent imaginary unit, CS represents the pseudo random sequence of the plural form after combination, and its length is N;
According to the definition of correlation function, the correlation function of formula (8) is:
The real part of described correlation function
be expressed as:
The imaginary part of described correlation function
be expressed as:
Wherein, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance; I ≠ j then describes their cross correlation.
As the further improvement of technique scheme, obtaining spread spectrum transmission signal indication in described step 5) is:
Wherein, T
_{c}represent the duration of the single chip of pseudo random sequence, t represents the time,
expression information chip,
with
represent sequence,
represent the pseudo random sequence of the plural form after combination, ω is carrier angular frequencies,
for carrier wave initial phase, T
_{d}represent the time that single information sequence continues.
As the further improvement of technique scheme, described " complementary series " is to employing LS code.
A kind of advantage of the direct sequence spread spectrum modulator approach of Multipath interference in underwater sound communication that suppresses of the present invention is:
Employing of the present invention " complementary series ", to as the pseudo random sequence in underwater sound spreadspectrum communication, can construct desirable autocorrelation and crosscorrelation function, can suppress the Multipath interference in underwater sound spreadspectrum communication in theory completely; The combined method that two kinds " complementary series " is right is provided, can selects as the case may be during use: 1) timedivision Orthogonal Composite mode: the value of adding between complementary series be 0 sequence can reduce transmitting duty ratio, thus play the effect of cooling power amplifier; Insensitive to carrier phase during this signal employing quadrature demodulation, do not need accurate carrier phase synchronization; When signal to noise ratio is lower, the demodulation bit error rate of the method is better than mode 2); 2) carrier phase Orthogonal Composite mode: the information transmitting efficiency of the method is consistent with the common pseudo random sequence band spectrum modulation such as m sequence, Gold sequence, than mode 1) efficiency is higher; When signal to noise ratio is higher, the demodulation bit error rate of the method is better than mode 1).
Accompanying drawing explanation
Fig. 1 is a kind of flow chart suppressing the direct sequence spread spectrum modulator approach of Multipath interference in underwater sound communication of the present invention.
Fig. 2 is the structural representation that in the present invention, " complementary series " generates pseudo random sequence to employing time division way Orthogonal Composite.
Fig. 3 is the autocorrelation function adopting time division way Orthogonal Composite to generate pseudo random sequence in the present invention.
Fig. 4 is the crosscorrelation function adopting time division way Orthogonal Composite to generate pseudo random sequence in the present invention.
Fig. 5 is the autocorrelation function adopting carrier phase orthogonal manner Orthogonal Composite to generate pseudo random sequence in the present invention.
Fig. 6 is the crosscorrelation function adopting carrier phase orthogonal manner Orthogonal Composite to generate pseudo random sequence in the present invention.
Fig. 7 is the lake examination CZT timefrequency search graphics of the spread spectrum transmission signal obtained based on time division way in the present invention.
Fig. 8 is the lake examination CZT timefrequency search graphics of the spread spectrum transmission signal obtained based on carrier phase orthogonal manner in the present invention.
Embodiment
Below in conjunction with drawings and Examples, a kind of direct sequence spread spectrum modulator approach of Multipath interference in underwater sound communication that suppresses of the present invention is described in detail.
As shown in Figure 1, a kind of direct sequence spread spectrum modulator approach suppressing Multipath interference in underwater sound communication of the present invention, described direct sequence spread spectrum modulator approach comprises:
Step 1) constructs two and meets " complementary series " to the sequence A code of relation and B code, i.e. two sequences orthogonal sequence each other, and A code aperiodic autocorrelation or the autocorrelation of crosscorrelation function and B code or crosscorrelation function equal at zero propagation place, equal at other local absolute values, symbol is contrary;
Step 2) two sequences obtained in step 1) are carried out Orthogonal Composite generation pseudo random sequence, using this pseudo random sequence as spreading code;
Step 3), according to the transmission bandwidth of spreadspectrum signal, calculates the duration of single spreading code chip, according to the rate of information throughput, calculates the duration of single information chip, then calculates the chip number of the spreading code corresponding to single information chip;
Step 4) according to the result calculated in step 3), by the information chip launched according to corresponding number relation respectively with step 2) in after the pseudo random sequence that obtains does mould 2 multiplication operation, combination producing complex base band spreadspectrum signal;
The complex base band spreadspectrum signal obtained in step 4) is multiplied with signal carrier and gets real part by step 5), obtains spread spectrum transmission signal.
Based on abovementioned direct sequence spread spectrum modulator approach, the length of hypothetical sequence is all N, then meet " complementary series " and can be expressed as on continuoustime domain two of relation sequences:
Wherein, t represents the time, c
_{n}represent the sequential value of the nth pseudo random sequence, rect () is square wave function
t
_{c}represent the duration of the single chip of pseudo random sequence.
The correlation function that described " complementary series " is right may be defined as:
Wherein, τ represents sequence A
_{i}and A
_{j}time delay, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance; I ≠ j then describes their cross correlation.As can be seen from formula (2), " complementary series " is all desirable to the autocorrelation of the correlation function constructed and their cross correlation, and namely autocorrelation has individual pulse in 0 time delay place; Outside 0 time delay, autocorrelation and crosscorrelation are all 0.
In addition, the information chip launched in described step 4) can be expressed as:
Wherein, d
_{n}represent the nth information sequence value, t represents the time, T
_{d}represent the time that single information sequence continues.
Signal carrier in described step 5) can be expressed as:
Wherein,
represent imaginary unit, ω is carrier angular frequencies,
for carrier wave initial phase, t represents the time.In the present invention, " complementary series " that can be used as pseudo random sequence to and building method have a lot.In the present embodiment, for LS code, as " complementary series " of underwater sound spreadspectrum communication to spreading code.Suppose (c
_{n}, s
_{n}) and (c '
_{n}, s '
_{n}) be that as N=2, basic complementary series can be expressed as code character with group complementary series pair:
According to following treelike iteration, iteration each time, can obtain complementary series that length doubles to code character.
Through n expansion, can 2 be obtained
^{n}be 2 to code length
^{n}" complementary series " of N is right.
Because the nonperiodic autocorrelation function of C code is equal at zero propagation place with the autocorrelation function of S code, equal at other local absolute values, symbol is contrary.Therefore, C code and S code are combined by certain mode, in the interval of orthogonality of C code and S code, correlation function superposes, and is formed " zero correlation window ", forms LS code thus.
In order to the sequence A code of " complementary series " centering and B code (sequential value of A code and B code can only get+1 or1) are constructed ideal correlation function in zero correlation window, need to ensure that sequence A code and B code can not occur related operation, namely sequence A code and B code reach orthogonal in some sense.In order to reach orthogonal object when modulating, The present invention gives two kinds of feasible methods:
1) time division way: by the sequence A code of " complementary series " centering and the sequencing arrangement temporally of B code, the value adding certain length between sequence A code and B code is the sequence of 0, and the Orthogonal Composite realizing two sequence A codes and B code thus generates pseudo random sequence.The structure of pseudo random sequence as shown in Figure 1 can be expressed as:
Wherein, A
_{n}and B
_{n}represent sequence, W represents the number of add between two sequences 0, and S represents pseudo random sequence, and its length is 2 (N+W);
According to the definition of correlation function, the correlation function of formula (7) is expressed as:
Wherein, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance; I ≠ j then describes their cross correlation.
Obviously, when time delay  τ  during < W, adopt " complementary series " of time division way Orthogonal Composite can obtain desirable correlation function to the pseudo random sequence formed.
2) carrier phase orthogonal manner: the sequence A code of " complementary series " centering and B code are adjusted to respectively on two quadrature carriers that phase is 90 degree, the Orthogonal Composite realizing two sequences thus generates pseudo random sequence.The pseudo random sequence obtained can be expressed as:
CS＝A
_{n}+jB
_{n}（9）
Wherein, A
_{n}and B
_{n}represent sequence,
represent imaginary unit, CS represents the pseudo random sequence of the plural form after combination, and its length is N;
According to the definition of correlation function, the correlation function of formula (9) is expressed as:
The real part of correlation function
be expressed as:
The imaginary part of correlation function
be expressed as:
Wherein, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance; I ≠ j then describes their cross correlation.
Obviously, as can be seen from the real part correlation function of formula (11), adopt " complementary series " of carrier phase orthogonal manner Orthogonal Composite to the pseudo random sequence formed, the real part of its correlation function, any time delay has desirable autocorrelation and crosscorrelation function.
As can be seen from formula (12), the imaginary part of the correlation function of the spreading code of carrier phase orthogonal manner Orthogonal Composite is adopted to represent the result of the crosscorrelation effect of " complementary series " centering sequence A code and B code, although its value is not constantly equal to 0 in any delay time section, but due to sequence A code and B code orthogonal, therefore the amplitude of imaginary part is very little, also very little on the impact of whole correlation function.In order to make full use of the desirable correlation properties of combinational code, for the correlation demodulation of this spreading code, only need the real part taking out correlated results as effective Output rusults.
According to the direct sequence spread spectrum modulation system of spreadspectrum signal, when dividing mode when employed, the spread spectrum transmission signal indication obtained in conjunction with formula (1), (3) and (7) is:
When adopting carrier phase orthogonal manner, the spread spectrum transmission signal indication obtained in conjunction with formula (1), (3) and (9) is:
According to the basic theories of spread spectrum communication, suppose the pseudorandom spreading sequence having at least one complete in 1 information chip, the correlation properties of spread spectrum transmission signal in base band then calculated by formula (13) and formula (14), are determined by the correlation function of formula (3) and formula (4) respectively.
Below in conjunction with the actual transmit signal that certain lake is tried, the specific embodiment of the present invention is described in further detail.
The spread spectrum transmission signal parameter based on LS code that experiment is launched is as follows:
Signal bandwidth: 4KHz ~ 8KHz, centre frequency: 6KHz.
Step 201): generate " complementary series " right sequence A code and B code, this step can according to the iterative manner of formula (5) and (6), and required for generating, " complementary series " of length is to C code and S code.
Step 202): according to step 201) in " complementary series " to C code and S code carry out Orthogonal Composite generate pseudo random sequence, obtain two kinds of pseudorandom spreading sequence: the C code and the S code that 1) generate 512 chip lengths, insert 0 of 512 chips at C code and S intersymbol, be combined into according to timedivision orthogonal form the spreading code that length is 2048 chips; 2) generate C code and the S code of 1024 chip lengths, be combined into according to carrier phase orthogonal form the multiple spreading code that length is 1024 chips.
Step 203): according to the transmission bandwidth of spreadspectrum signal, calculate the duration T of single spreading code chip
_{c}; According to the rate of information throughput, calculate the duration T of single information chip
_{d}; Then the chip number of frequency expansion sequence corresponding to single information chip is calculated.
Step 204): according to step 203) result that calculates, by the information chip launched according to corresponding number relation respectively with step 202) in two kinds of pseudorandom spreading sequence obtaining do mould 2 multiplication operation, and according to the syntagmatic that formula (7) and (9) provide, combination producing complex base band spreadspectrum signal.
Step 205: carry out direct sequence spread spectrum modulation according to formula (13) or (14), is multiplied complex base band spreadspectrum signal with signal carrier and gets real part, obtaining spread spectrum transmission signal.
As Fig. 3 and Fig. 4 shows according to the examination experiment of abovementioned lake, time division way Orthogonal Composite is adopted to generate autocorrelation and the cross correlation results of pseudo random sequence, it is that the C code of 512 chips and S code combine according to the form that the timedivision is orthogonal by length, inserts 0 of 512 chip lengths between C code and S code.As we know from the figure, the interval of the zero correlation window (IFW) of formation is (512,512), and in zero correlation window, combinational code has desirable autocorrelation and crosscorrelation function.
As Fig. 5 and Fig. 6 shows according to the examination experiment of abovementioned lake, adopt carrier phase orthogonal manner Orthogonal Composite to generate autocorrelation and the cross correlation results of pseudo random sequence, it is that the C code of 1024 chips and S code combine according to the form of real part and imaginary part by length.As we know from the figure, in any time delay, the real part of this combinational code correlation function has desirable autocorrelation and cross correlation value, and it is consistent with the notional result described by formula (11).
As Fig. 7 and Fig. 8 shows according to the examination experiment of abovementioned lake, the threedimensional result that two kinds " complementary series " is doing the search of CZT timefrequency obtain the spreadspectrum signal of combinational code.Can find out, the region outside the main peak of Search Results is very smooth, this means that two kinds of spreadspectrum signals can have good correlation properties, can reach good multipath signals rejection ability.
It should be noted last that, above embodiment is only in order to illustrate technical scheme of the present invention and unrestricted.Although with reference to embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that, modify to technical scheme of the present invention or equivalent replacement, do not depart from the spirit and scope of technical solution of the present invention, it all should be encompassed in the middle of right of the present invention.
Claims (9)
1. suppress a direct sequence spread spectrum modulator approach for Multipath interference in underwater sound communication, it is characterized in that, described direct sequence spread spectrum modulator approach comprises:
Step 1) constructs two and meets " complementary series " to the sequence of relation;
Step 2) two sequences obtained in step 1) are carried out Orthogonal Composite generation pseudo random sequence, using this pseudo random sequence as spreading code;
Step 3) is according to the transmission bandwidth of spreadspectrum signal, calculate the duration of single spreading code chip, according to the rate of information throughput, calculate the duration of single information chip, then calculate corresponding to single information chip from step 2) the chip number of spreading code that obtains;
Step 4) according to the result calculated in step 3), by the information chip launched according to corresponding number relation respectively with step 2) in after the pseudo random sequence that obtains does mould 2 multiplication operation, combination producing complex base band spreadspectrum signal;
The complex base band spreadspectrum signal obtained in step 4) is multiplied with signal carrier and gets real part by step 5), obtains spread spectrum transmission signal.
2. the direct sequence spread spectrum modulator approach of Multipath interference in suppression underwater sound communication according to claim 1, it is characterized in that, each sequence generated in step 1) is expressed as on continuoustime domain:
Wherein, the length of sequence is that N, t represent the time, c
_{n}represent the sequential value of the nth pseudo random sequence, rect () is square wave function
t
_{c}represent the duration of the single chip of pseudo random sequence;
The correlation function that described " complementary series " is right is defined as:
Wherein, τ represents sequence A
_{i}and A
_{j}time delay, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance, and i ≠ j then describes their cross correlation.
3. the direct sequence spread spectrum modulator approach of Multipath interference in suppression underwater sound communication according to claim 1, it is characterized in that, the information chip launched in described step 4) is expressed as:
Wherein, d
_{n}represent the nth information sequence value, t represents the time, T
_{d}represent the time that single information sequence continues.
4. the direct sequence spread spectrum modulator approach of Multipath interference in suppression underwater sound communication according to claim 1, it is characterized in that, the signal carrier in described step 5) is expressed as:
Wherein,
represent imaginary unit, ω is carrier angular frequencies,
for carrier wave initial phase, t represents the time.
5. the direct sequence spread spectrum modulator approach of Multipath interference in suppression underwater sound communication according to claim 1, it is characterized in that, described step 2) middle Orthogonal Composite generation pseudo random sequence employing time division way, after two sequences sequencing is temporally arranged, the value adding certain length between two sequences is the sequence of 0, and the pseudo random sequence obtained is expressed as:
Wherein, A
_{n}and B
_{n}represent sequence, W represents the number of add between two sequences 0, and S represents pseudo random sequence, and its length is 2 (N+W);
According to the definition of correlation function, the correlation function of formula (5) is expressed as:
Wherein, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance, and i ≠ j then describes their cross correlation.
6. in the suppression underwater sound communication according to claim 2,3,4 or 5, the direct sequence spread spectrum modulator approach of Multipath interference, is characterized in that, obtains spread spectrum transmission signal indication to be in described step 5):
Wherein, T
_{c}represent the duration of the single chip of pseudo random sequence, t represents the time,
expression information chip,
with
represent sequence, ω is carrier angular frequencies,
for carrier wave initial phase, T
_{d}represent the time that single information sequence continues.
7. the direct sequence spread spectrum modulator approach of Multipath interference in suppression underwater sound communication according to claim 1, it is characterized in that, described step 2) middle Orthogonal Composite generation pseudo random sequence employing carrier phase orthogonal manner, two sequences be adjusted to respectively on the quadrature carrier that phase is 90 degree, the pseudo random sequence obtained is expressed as:
CS＝A
_{n}+jB
_{n}（8）
Wherein, A
_{n}and B
_{n}represent sequence,
represent imaginary unit, CS represents the pseudo random sequence of the plural form after combination, and its length is N;
According to the definition of correlation function, the correlation function of formula (8) is:
The real part of described correlation function
be expressed as:
The imaginary part of described correlation function
be expressed as:
Wherein, A
_{i}, A
_{j}, B
_{i}, B
_{j}be the pseudo random sequence of satisfied " complementary series " relation, as i=j, above formula describes autocorrelation performance, and i ≠ j then describes their cross correlation.
8. in the suppression underwater sound communication according to claim 2,3,4 or 7, the direct sequence spread spectrum modulator approach of Multipath interference, is characterized in that, obtains spread spectrum transmission signal indication to be in described step 5):
Wherein, T
_{c}represent the duration of the single chip of pseudo random sequence, t represents the time,
expression information chip,
with
represent sequence,
represent the pseudo random sequence of the plural form after combination, ω is carrier angular frequencies,
for carrier wave initial phase, T
_{d}represent the time that single information sequence continues.
9. the direct sequence spread spectrum modulator approach of Multipath interference in suppression underwater sound communication according to claim 1, is characterized in that, described " complementary series " is to employing LS code.
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