CN114039825A - SIMO-HPO-CDSK communication method based on Rayleigh fading channel - Google Patents

SIMO-HPO-CDSK communication method based on Rayleigh fading channel Download PDF

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CN114039825A
CN114039825A CN202111349998.2A CN202111349998A CN114039825A CN 114039825 A CN114039825 A CN 114039825A CN 202111349998 A CN202111349998 A CN 202111349998A CN 114039825 A CN114039825 A CN 114039825A
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cdsk
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段俊毅
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Nanjing Institute of Railway Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2668—Details of algorithms
    • H04L27/2681—Details of algorithms characterised by constraints
    • H04L27/2686—Range of frequencies or delays tested
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2668—Details of algorithms
    • H04L27/2681—Details of algorithms characterised by constraints
    • H04L27/2688—Resistance to perturbation, e.g. noise, interference or fading

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Abstract

The invention discloses a SIMO-HPO-CDSK communication method based on Rayleigh fading channels, which comprises the following steps: s1, building an HPO-CDSK system model, S2, building a SIMO-HPO-CDSK system model, S3, analyzing HPO-CDSK performance, S4, analyzing SIMO-HPO-CDSK performance, S5, simulating experiments and analyzing results; the theoretical BER expression of the SIMO-HPO-CDSK is analyzed by adopting Gaussian approximation analysis under the conditions of an AWGN channel and a Rayleigh fading channel respectively, simulation is carried out, signal internal interference is eliminated when a receiving end demodulates, the BER performance of the SIMO-HPO-CDSK is superior to that of DCSK, CDSK and HE-DCSK, the SIMO-HPO-CDSK can transmit 2 bits of information at the same time in the same time slot, the spectrum utilization rate of the SIMO-HPO-CDSK is 2 times that of the CDSK, DCSK, HE-DCSK and PO-CDSK, and in addition, the BER performance of the SIMO-HPO-CDSK is further reduced along with the increase of the number of receiving antennas.

Description

SIMO-HPO-CDSK communication method based on Rayleigh fading channel
Technical Field
The invention relates to the technical field of communication methods, in particular to a SIMO-HPO-CDSK communication method based on a Rayleigh fading channel.
Background
Due to the advantages of non-periodicity, wide frequency spectrum, good correlation, similar noise and the like, the chaotic signal is widely applied to the field of spread spectrum digital communication systems. Some studies also show that the chaotic technology can be used for digital modulation systems and cognitive radio networks and enhance the safety of the digital modulation systems and the cognitive radio networks. Chaotic communication systems are generally classified into two types, coherent and incoherent chaotic communication systems. By applying carrier recovery techniques at the receiver demodulation, the coherent method has a lower Bit-error-rate (BER). However, due to noise interference, a synchronization mechanism, which is critical to carrier recovery, has poor performance in a coherent chaotic communication system. Therefore, the incoherent chaotic communication method without chaotic synchronization on the receiver is gradually the research focus of many scholars.
As a classical non-coherent chaotic communication modulation, kolomb' n first proposed Differential Chaos Keying (DCSK) in 1996. Since the bandwidth efficiency is only half of that of the coherent chaotic communication method and the hardware stability is low, many modified DCSK versions have been proposed in recent decades. For example, orthogonal-Chaos-Shift-Keying (QCSK) and Multi-Carrier DCSK (MC-DCSK) systems sacrifice hardware complexity to increase data rates. Although High-Efficiency DCSK (HE-DCSK) and Reference-Modulated DCSK (RM-DCSK) have good performance in terms of transmission rate, security, and system complexity, more intra-signal interference (ISI) is generated in the decision variables, which results in degradation of BER performance.
In order to improve the bandwidth efficiency of DCSK, sushcik proposed "Correlation-Delay-Shift-Keying (CDSK)" in 2000. However, the cost that CDSK must pay is still ISI interference. General-purpose CDSK (Generalized CDSK, GCDSK) enhances the useful signal component by adding more delay blocks, reducing the impact of ISI components on decision variables, but the system complexity is high. For this reason, the present invention has been made.
Disclosure of Invention
The invention aims to solve the problems, designs a SIMO-HPO-CDSK communication method based on a Rayleigh fading channel and solves the problems of the prior art.
The technical method for realizing the aim comprises the following steps: the SIMO-HPO-CDSK communication method based on the Rayleigh fading channel comprises the following steps: s1, building an HPO-CDSK system model, S2, building a SIMO-HPO-CDSK system model, S3, analyzing HPO-CDSK performance, S4, analyzing SIMO-HPO-CDSK performance, S5, simulating experiments and analyzing results;
step S1: complex of HPO-CDSKThe frame structure is similar to PO-CDSK, and comprises (theta +1) equal frames in a multiframe; one frame comprises beta equal time slots, wherein beta represents a spreading factor; in the k-th time slot, the chaotic signal is x (t) ═ xkhT(t),kTC≤t＜(k+1)TC；
xkIs a sequence from a chaotic generator, Tc is the period of a time slot, hT(t) is the impulse response of the square-root raised cosine filter, hT(t) has a specific energy of
Figure BDA0003355522450000021
Two reference signals are transmitted simultaneously in a frame, so that the information symbol d is obtained in the transmitted signal s (t)1,δ,lAnd d2,δ,lDeriving an expression for the transmitted signal s (t) during the l-th frame;
assuming that the transmitted signal is disturbed by Additive White Gaussian Noise (AWGN), the received signal is expressed as r (t) ═ s (t) + ξ (t), where ξ (t) is independent and uniformly distributed zero-mean gaussian noise, at the receiver, the delayed signal will be used as reference component for demodulation, during the l-th frame of the δ -th multiframe, the relevant output expression is derived, the estimated information symbol is decided as "+ 1" or "-1";
step S2: a plurality of antennas are distributed to a receiver end, and because the receiving end adopts a plurality of antennas, a plurality of relatively independent channels are formed between the transmitting antenna and the receiving antenna, which means that the channel state is kept constant in each transmission period;
in the SIMO-HPO-CDSK system, we assume that all channels satisfy the same rayleigh fading channel condition, and therefore, the received signal at the ith receiving antenna can be represented as follows: r isi(t)＝hi(t)s(t)+ξi(t); wherein h isi(t) and xii(t) is the channel parameter between the transmitter antenna and the ith receiver antenna, hi(t) is an independent, Rayleigh-distributed random variable, ξi(t) is white gaussian noise independently and identically distributed;
under the Rayleigh fading channel model, the ith correlator output of the SIMO-HPO-CDSK system is
Figure BDA0003355522450000022
And
Figure BDA0003355522450000023
d can be determined by summing the equal gains of the HPO-CDSK demodulator outputs of the various branches1,δ,lAnd d2,δ,l. Under Rayleigh fading channel model, y1,δ,lAnd y2,δ,lCan be deduced as
Figure BDA0003355522450000024
And
Figure BDA0003355522450000025
will y1,δ,lAnd y2,δ,lJudging to obtain information output;
step S3: for the Chebyshev mapping, the condition is expected to be E [ y ]1,δ,l]＝βd1,δ,lE[μ]＝βd1,δ,lPsE[y2,δ,l]＝βd2,δ,lE[μ]＝βd2,δ,lPsDeducing a BER formula output by the HPO-CDSK correlator under an AWGN channel by adopting a Gaussian approximation analysis method;
step S4: according to the expressions of y1, delta, l and y2, delta, l in the SIMO-HPO-CDSK, under the Chebyshev mapping condition, a BER formula output by the SIMO-HPO-CDSK correlator under the AWGN channel environment is obtained, and the BER formula output by the SIMO-HPO-CDSK correlator under the Rayleigh fading channel is derived on the basis of a channel fading parameter set in the Rayleigh fading channel.
Step S5: to verify the performance analysis in the upper section, this section compares the simulation results of BER under various channel conditions with the analysis results in the second section.
In the modulation mechanism of the HPO-CDSK in step S1, three cases should be considered;
1) when l is 0, during even multiframes, T1 is connected to the middle branch, T2 is connected to the bottom branch, cosine wave (cos2 pi f)0t) multiplied by the output of the chaotic generator x (t), x (t) cos2πf0t is transmitted as a transmission signal to the transmitter antenna and the two delay blocks;
2) when l is 0, during odd multiframes T1 and T2 are synchronously connected to the bottom branch, a sine wave (sin2 pi f)0t) multiplication with the output of the chaotic generator x (t), x (t) sin2 π f0t is transmitted as a transmission signal to the transmitter antenna and the two delay blocks;
3) when 1 ≦ l ≦ θ, T1 and T2 are synchronously connected to the top branch, and during the δ -th multiframe, the chaotic sequence transmitted in the first frame is used as a reference signal to carry the information symbol d1,δ,l. Since the time interval between two time delay blocks is theta frame, the chaotic sequence transmitted in frame 1 of the delta-th multiframe is used as a reference signal for carrying the information symbol d2,δ,l。
In step S2, the receiver uses an Equal Gain Combiner (EGC) to obtain performance gain.
In step S3, the correlator outputs (y1, δ, l and y2, δ, l) are described as follows: calculating to obtain y when delta is odd number or even number1,δ,lAnd y2,δ,lThe conditional variance of (c).
All independent channels in the step S4 satisfy the same rayleigh fading channel condition.
The parameters used in the SIMO-HPO-CDSK system in the step S5 are the same as those used in the conventional CDSK system by using 3-order Chebyshev mapping, that is, the parameters are xk+1＝4xk 3-3xkGenerating different chaotic sequences, the initial value x00.1, the average power gain of each Rayleigh fading channel is E [ h [ ]i 2]＝1。
The SIMO-HPO-CDSK communication method based on the Rayleigh fading channel adopts a Gaussian approximation analysis method to respectively carry out derivation analysis on a theoretical BER expression of the SIMO-HPO-CDSK under the conditions of an AWGN channel and the Rayleigh fading channel, and carries out simulation, internal interference of signals is eliminated when a receiving end demodulates, the BER performance of the SIMO-HPO-CDSK is superior to that of DCSK, CDSK and HE-DCSK, the SIMO-HPO-CDSK can simultaneously transmit 2 bits of information in the same time slot, the spectrum utilization rate of the SIMO-HPO-CDSK is 2 times that of the CDSK, the DCSK, HE-DCSK and PO-CDSK, and in addition, the BER performance of the SIMO-HPO-CDSK is further reduced along with the increase of the number of receiving antennas.
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Fig. 1 is a multi-frame structure diagram of the SIMO-HPO-CDSK communication method based on rayleigh fading channel according to the present invention.
Fig. 2 is a block diagram of an HPO-CDSK transmitter of the SIMO-HPO-CDSK communication method based on rayleigh fading channels according to the present invention.
Fig. 3 is a block diagram of a HPO-CDSK receiver of the SIMO-HPO-CDSK communication method based on rayleigh fading channel according to the present invention.
FIG. 4 is a block diagram of the SIMO-HPO-CDSK communication method based on the Rayleigh fading channel according to the invention.
FIG. 5 is a diagram comparing the SIMO-HPO-CDSK theory and simulation performance under the AWGN channel of the SIMO-HPO-CDSK communication method based on Rayleigh fading channel.
FIG. 6 is a diagram of comparing the SIMO-HPO-CDSK with the CDSK and DCSK performances under the AWGN channel of the SIMO-HPO-CDSK communication method based on Rayleigh fading channel of the present invention.
FIG. 7 is a diagram of comparing the SIMO-HPO-CDSK performance with HE-DCSK and PO-CDSK performance under AWGN channel of the SIMO-HPO-CDSK communication method based on Rayleigh fading channel.
FIG. 8 is a diagram of SIMO-HPO-CDSK performance under the Rayleigh fading channel in the SIMO-HPO-CDSK communication method based on the Rayleigh fading channel of the present invention.
FIG. 9 is a diagram of comparing the performance of the SIMO-HPO-CDSK with the performance of the CDSK and the performance of the DCSK under the Rayleigh fading channel in the SIMO-HPO-CDSK communication method based on the Rayleigh fading channel.
FIG. 10 is a diagram of comparing the performance of SIMO-HPO-CDSK with HE-DCSK and PO-CDSK under Rayleigh fading channel in the SIMO-HPO-CDSK communication method based on Rayleigh fading channel of the present invention.
Detailed Description
SIMO-HPO-CDSK will be introduced in this section. Assuming that all independent channels satisfy the same rayleigh fading channel and the same gaussian distributed random noise, and the power spectral density is N0. Reception in the systemThe end adopts branch Equal Gain Combination (EGC), which not only can improve the error performance, but also is easy to realize.
Step one, building an HPO-CDSK system model
Fig. 1 is a multiframe structure of HPO-CDSK. Similar to PO-CDSK, (θ +1) equal frames are contained in one multiframe. A frame contains β equal slots, β representing the spreading factor.
Fig. 2 is a transmitter structure of HPO-CDSK. In the k-th time slot, the chaotic signal is
x(t)＝xkhT(t),kTC≤t＜(k+1)TC (1)
Where xk is the sequence from the chaotic generator, Tc is the period of a time slot, hT (t) is the impulse response of the square root raised cosine filter, hT (t) has a specific energy of
Figure BDA0003355522450000041
To illustrate the modulation mechanism of HPO-CDSK, we consider three conditions below:
1) when l is 0, during even multiframes, T1 is connected to the middle branch, T2 is connected to the bottom branch, the cosine wave (cos2 pi f0T) is multiplied by the output of the chaos generator x (T), x (T) cos2 pi f0T is sent as a transmit signal to the transmitter antenna and to the two delay blocks.
2) When l is 0, during odd multiframes, T1 and T2 are synchronously connected to the bottom branch, a sine wave (sin2 pi f0T) is multiplied by the output of the chaotic generator x (T), x (T) sin2 pi f0T is sent as a transmit signal to the transmitter antenna and to the two delay blocks.
3) When 1 ≦ l ≦ θ, T1 and T2 are synchronously connected to the top branch, and the chaotic sequence transmitted in the first frame is used as a reference signal during the δ -th multiframe to carry the information symbols d1, δ, l. Since the time interval between two time delay blocks is θ frames, the chaotic sequence transmitted in frame 1 of the δ -th multiframe is used as a reference signal for carrying the information symbols d2, δ, l.
As described above, since two reference signals are simultaneously transmitted in one frame, information symbols d1, δ, l and d2, δ, l are derived in the transmission signal s (t).
In fig. 2, the expression of the transmission signal s (t) during the l-th frame is given by equation (3).
Figure BDA0003355522450000051
Where f0 represents the frequency of sine and cosine waves, and satisfies not only a multiple of 1/Tc but also f0> > (1/Tc).
Fig. 3 is a block diagram of an HPO-CDSK receiver, where two delay lines are used to synchronously demodulate 2-bit information.
Assuming that a transmission signal is interfered by Additive White Gaussian Noise (AWGN), a reception signal is expressed as
r(t)＝s(t)+ξ(t) (4)
Where ξ (t) is an independent and uniformly distributed zero-mean gaussian noise.
At the receiver, the delayed signal will be used as a reference component for demodulation. During the l-th frame of the delta-th multiframe, the correlator output is expressed as
Figure BDA0003355522450000052
Figure BDA0003355522450000053
The estimated information symbol is decided as "+ 1" or "-1" according to the rules shown in equations (5) and (6).
Figure BDA0003355522450000054
Figure BDA0003355522450000055
Step two, SIMO-HPO-CDSK system model construction
FIG. 4 is a block diagram of a SIMO-HPO-CDSK system. In this system, we consider that a plurality of antennas are allocated to the receiver side. As shown, the transmitter is identical to the HPO-CDSK. Since the receiving end adopts multiple antennas, multiple relatively independent channels are formed between the transmitting antenna and the receiving antenna, which means that the channel state is kept constant in each transmission period.
In the SIMO-HPO-CDSK system, we assume that all channels satisfy the same rayleigh fading channel conditions. Therefore, the received signal at the ith receive antenna can be represented as follows:
ri(t)＝hi(t)s(t)+ξi(t) (9)
where hi (t) and ξ i (t) are the channel parameters between the transmitter antenna and the ith receiver antenna, hi (t) is an independent, rayleigh distributed random variable, and ξ i (t) is independent, identically distributed gaussian white noise.
The ith correlator output of the SIMO-HPO-CDSK system under the Rayleigh fading channel model using the expression shown in equation (9) is
Figure BDA0003355522450000061
Figure BDA0003355522450000062
To obtain performance gain, the receiver employs an Equal Gain Combiner (EGC), as shown in fig. 5. Thus, d1, δ, l and d2, δ, l can be determined by summing the gains of the HPO-CDSK demodulator outputs etc. of the individual branches. Under the Rayleigh fading channel model, the expressions of y1, delta, l and y2, delta, l can be derived as
Figure BDA0003355522450000063
Figure BDA0003355522450000064
Where n is the number of receive antennas. As shown in equations (7) and (8), the information output can be obtained by deciding y1, δ, l and y2, δ, l.
Step three, HPO-CDSK performance analysis
To facilitate the analysis of fig. 2, based on equations (5) and (6), the correlator outputs (y1, δ, l and y2, δ, l) can be illustrated as follows:
1. if delta is an even number
(1) y1, δ, l can be expressed as equation (14)
Figure BDA0003355522450000065
Wherein A, γ, and ζ can be written as equations (15) to (17)
Figure BDA0003355522450000066
Figure BDA0003355522450000071
Figure BDA0003355522450000072
(2) y2, δ, l can be expressed as equation (18)
Figure BDA0003355522450000073
Wherein A, γ, ζ can be written as equation (19) (21)
Figure BDA0003355522450000074
Figure BDA0003355522450000075
Figure BDA0003355522450000076
2. If delta is an even number
(1) y1, δ, l can be expressed as equation (22)
Figure BDA0003355522450000077
Wherein A, γ, and ζ can be written as equations (15) to (17)
Figure BDA0003355522450000081
Figure BDA0003355522450000082
Figure BDA0003355522450000083
(2) y2, δ, l can be expressed as equation (26)
Figure BDA0003355522450000084
Wherein A, γ, and ζ can be written as equations (27) to (29)
Figure BDA0003355522450000085
Figure BDA0003355522450000086
Figure BDA0003355522450000087
In equations (13) to (29), a is a useful signal component, γ is an ISI component, and ζ is a noise interference component. Similar to [14], since f0 is a multiple of (1/TC) and f0> > (1/TC),
Figure BDA0003355522450000088
where m and n are integers having values from l to (l + θ +1), 1 ≦ l ≦ θ, and m ≠ n. From the equation, considering the ISI components in the aforementioned correlator outputs (equations (14), (18), (22), (26)), it can be seen based on equation (30): during demodulation, intra-signal interference can be completely eliminated.
We know that:
Figure BDA0003355522450000091
ξ (t) is zero-mean stationary Gaussian noise with a power spectral density of N0/2. Chebyshev mapping is widely used in many chaotic communication methods [16], such as HE-DCSK, I-DCSK and MC-DCSK. For the Chebyshev mapping, the conditions are expected to be
E[y1,δ,l]＝βd1,δ,lE[μ]＝βd1,δ,lPs (32)
E[y2,δ,l]＝βd2,δ,lE[μ]＝βd2,δ,lPs (33)
As shown in [17], based on equation (31), in equations (32) and (33),
Figure BDA0003355522450000092
Figure BDA0003355522450000093
from equations (14), (18), (22) and (26), the conditional variances of y1, δ, l and y2, δ, l can be found:
Figure BDA0003355522450000094
Figure BDA0003355522450000095
wherein
Figure BDA0003355522450000096
In contrast to CDSK, we find that ISI components are removed in equations (36) and (37). However, since 2-bit information is transmitted in one slot, the noise component is carried slightly higher than that of PO-CDSK.
When β is large, the correlator output (equations (32) to (38)) can be approximated to a gaussian distribution. Adopting a Gaussian approximation analysis method [17-18], under an AWGN channel, the BER formula output by the HPO-CDSK correlator is derived as follows:
Figure BDA0003355522450000097
where erfc () represents a complementary error function,
Figure BDA0003355522450000098
eb is the average bit energy E in a frameb＝βPs (41)
Step four, SIMO-HPO-CDSK performance analysis
AWGN channel
According to the expressions of y1, δ, l and y2, δ, l in SIMO-HPO-CDSK (equation (12) and equation (13)), the condition of the SIMO-HPO-CDSK correlator output in an AWGN channel environment under Chebyshev mapping conditions is expected to be
E[y1,δ,l]＝nβd1,δ,lE[μ]＝nβd1,δ,lPs (42)
E[y2,δ,l]＝nβd2,δ,lE[μ]＝nβd2,δ,lPs (43)
Based on equations (42) through (45), the BER output from the SIMO-HPO-CDSK correlator in AWGN channel sum is formulated as
Figure BDA0003355522450000101
Where n is the number of receive antennas. Eb and ψ are shown as equation (40) and equation (41), respectively.
Rayleigh fading channel
For rayleigh fading channels, the following statistical information can be easily obtained:
Figure BDA0003355522450000102
Figure BDA0003355522450000103
Figure BDA0003355522450000104
Figure BDA0003355522450000105
where H denotes a set of channel fading parameters.
Under Rayleigh fading channel, the BER formula of the output of the SIMO-HPO-CDSK correlator can be deduced
Figure BDA0003355522450000106
Wherein the content of the first and second substances,
Figure BDA0003355522450000111
since hi is a Rayleigh distributed random variable, a probability density function (pdf) of γ Λ can be obtained
Figure BDA0003355522450000112
Wherein
Figure BDA0003355522450000113
Figure BDA0003355522450000114
Figure BDA0003355522450000115
Where E [ hi2] is the average power gain for the ith channel. We can calculate the pdf of γ Λ as the same as the pdf of γ Λ assuming that all independent channels satisfy the same rayleigh fading channel conditions
Figure BDA0003355522450000116
Under Rayleigh fading channel, the BER performance of SIMO-HPO-CDSK is
Figure BDA0003355522450000117
Step five, simulation experiment and result analysis
To verify the performance analysis in the upper section, this section compares the simulation results of BER under various channel conditions with the analysis results in the second section. The parameters used in the SIMO-HPO-CDSK system are the same as those used in the conventional CDSK system. And (3) adopting 3-order Chebyshev mapping, namely generating different chaotic sequences by xk + 1-4 xk3-3xk, wherein the initial value x0 is 0.1, and the average power gain of each Rayleigh fading channel is E [ hi2] is 1. Systems having different numbers of reception antennas are set to HPO-CDSK (1,1), HPO-CDSK (1,2), and HPO-CDSK (1,3), respectively.
FIG. 5 is a graph comparing theoretical and simulated performance of SIMO-HPO-CDSK under AWGN channel conditions, where Eb/N0 changes from 0dB to 16dB, spreading factor β is set to 100, (T) represents theoretical value, and (S) represents simulated value. Obviously, under the AWGN channel condition, when the Eb/N0 value is small, the SIMO-HPO-CDSK performance is greatly influenced by Gaussian noise, and the BER is high. As the value of Eb/N0 is increased, the BER of SIMO-HPO-CDSK is reduced. Since there is no ISI component in the correlator output, the simulated curve fits well with the theoretical curve for different spreading factors, thus proving the validity of the derivation in section 2.
FIGS. 6 and 7 show BER comparisons between SIMO-HPO-CDSK and CDSK, DCSK, HE-DCSK and PO-CDSK under AWGN channel conditions. Because the SIMO-HPO-CDSK does not need a separate time slot to transmit the reference signal, the BER performance of the SIMO-HPO-CDSK is always better than that of the DCSK under the condition of the same spreading factor. Because there is no ISI component in the correlator output of SIMO-HPO-CDSK, the BER performance of SIMO-HPO-CDSK is better when the receiving antennas are the same compared to CDSK, HE-DCSK. Since more noise components are introduced when demodulating at the receiving end, the PO-CDSK performance is slightly better when the receiving antennas are the same. However, as the number of receive antennas increases, the BER performance of SIMO-HPO-CDSK will gradually exceed PO-CDSK. It is worth noting that since SIMO-HPO-CDSK can transmit 2 bits of information at the same time in the same time slot, the spectrum utilization rate is 2 times of CDSK, DCSK, HE-DCSK and PO-CDSK.
FIG. 8 is a bit error rate curve obtained by the SIMO-HPO-CDSK system in the Rayleigh fading channel through the Gaussian approximation analysis and Monte Carlo simulation. In the figure, the spreading factor β takes a value of 100. As can be seen from the figure, under rayleigh fading channel conditions, the theoretical result obtained by using gaussian approximation analysis (calculated according to equation (46)) is substantially consistent with the simulation result, and as the number of receiving antennas increases, the system BER continues to decrease. This is because the useful signal component in the demodulation process increases as the number of receiving-end antennas increases.
Fig. 9 and 10 show BER comparisons between HPO-CDSK and other methods on rayleigh fading channels. As shown above, the BER performance of SIMO-HPO-CDSK is better than that of DCSK, CDSK and HE-DCSK under the condition of the same number of receiving-end antennas due to less interference and higher energy efficiency. Although SIMO-HPO-CDSK has slightly worse BER performance than PO-CDSK under single receiving antenna condition, its band utilization rate is almost twice that of PO-CDSK. In addition, as the number of receiving antennas increases, the BER of SIMO-HPO-CDSK is further reduced.
In conjunction with multi-antenna technology, SIMO-HPO-CDSK communication methods are presented herein. A theoretical BER expression of SIMO-HPO-CDSK is analyzed by adopting a Gaussian approximation analysis method under the conditions of an AWGN channel and a Rayleigh fading channel respectively in a derivation mode, and simulation is carried out.
The BER performance of the SIMO-HPO-CDSK is better than that of DCSK, CDSK and HE-DCSK because the internal signal interference can be eliminated when the receiving end demodulates. Because the SIMO-HPO-CDSK can transmit 2 bits of information at the same time in the same time slot, the spectrum utilization rate is 2 times of that of the CDSK, the DCSK, the HE-DCSK and the PO-CDSK. In addition, as the number of receiving antennas increases, the BER performance of SIMO-HPO-CDSK will be further reduced.
The technical method only represents the preferable technical method of the technical method, and some changes which can be made to some parts by the technical personnel in the technical field represent the principle of the invention and belong to the protection scope of the invention.

Claims (6)

1. The SIMO-HPO-CDSK communication method based on the Rayleigh fading channel is characterized by comprising the following steps: s1, building an HPO-CDSK system model, S2, building a SIMO-HPO-CDSK system model, S3, analyzing HPO-CDSK performance, S4, analyzing SIMO-HPO-CDSK performance, S5, simulating experiments and analyzing results;
step S1: the structure of the multi-frame of the HPO-CDSK is similar to that of the PO-CDSKContains (theta +1) equal frames; one frame comprises beta equal time slots, wherein beta represents a spreading factor; in the k-th time slot, the chaotic signal is x (t) ═ xkhT(t),kTC≤t＜(k+1)TC；
xkIs a sequence from a chaotic generator, Tc is the period of a time slot, hT(t) is the impulse response of the square-root raised cosine filter, hT(t) has a specific energy of
Figure FDA0003355522440000011
Two reference signals are transmitted simultaneously in a frame, so that the information symbol d is obtained in the transmitted signal s (t)1,δ,lAnd d2,δ,lDeriving an expression for the transmitted signal s (t) during the l-th frame;
assuming that the transmitted signal is disturbed by Additive White Gaussian Noise (AWGN), the received signal is expressed as r (t) ═ s (t) + ξ (t), where ξ (t) is independent and uniformly distributed zero-mean gaussian noise, at the receiver, the delayed signal will be used as reference component for demodulation, during the l-th frame of the δ -th multiframe, the relevant output expression is derived, the estimated information symbol is decided as "+ 1" or "-1";
step S2: a plurality of antennas are distributed to a receiver end, and because the receiving end adopts a plurality of antennas, a plurality of relatively independent channels are formed between the transmitting antenna and the receiving antenna, which means that the channel state is kept constant in each transmission period;
in the SIMO-HPO-CDSK system, we assume that all channels satisfy the same rayleigh fading channel condition, and therefore, the received signal at the ith receiving antenna can be represented as follows: r isi(t)＝hi(t)s(t)+ξi(t); wherein h isi(t) and xii(t) is the channel parameter between the transmitter antenna and the ith receiver antenna, hi(t) is an independent, Rayleigh-distributed random variable, ξi(t) is white gaussian noise independently and identically distributed;
under the Rayleigh fading channel model, the ith correlator output of the SIMO-HPO-CDSK system is
Figure FDA0003355522440000012
And
Figure FDA0003355522440000013
d can be determined by summing the equal gains of the HPO-CDSK demodulator outputs of the various branches1,δ,lAnd d2,δ,l. Under Rayleigh fading channel model, y1,δ,lAnd y2,δ,lCan be deduced as
Figure FDA0003355522440000014
And
Figure FDA0003355522440000015
will y1,δ,lAnd y2,δ,lJudging to obtain information output;
step S3: for the Chebyshev mapping, the condition is expected to be E [ y ]1,δ,l]＝βd1,δ,lE[μ]＝βd1,δ,lPsE[y2,δ,l]＝βd2,δ,lE[μ]＝βd2,δ,lPsDeducing a BER formula output by the HPO-CDSK correlator under an AWGN channel by adopting a Gaussian approximation analysis method;
step S4: according to the expressions of y1, delta, l and y2, delta, l in the SIMO-HPO-CDSK, under the Chebyshev mapping condition, a BER formula output by the SIMO-HPO-CDSK correlator under the AWGN channel environment is obtained, and the BER formula output by the SIMO-HPO-CDSK correlator under the Rayleigh fading channel is derived on the basis of a channel fading parameter set in the Rayleigh fading channel.
Step S5: to verify the performance analysis in the upper section, this section compares the simulation results of BER under various channel conditions with the analysis results in the second section.
2. The method for SIMO-HPO-CDSK communication based on rayleigh fading channel according to claim 1, wherein the modulation scheme of HPO-CDSK in step S1 should consider three cases;
1) when l ═0, during even multiframes, T1 is connected to the middle branch, T2 is connected to the bottom branch, cosine wave (cos2 π f0t) multiplied by the output of the chaotic generator x (t), x (t) cos2 π f0t is transmitted as a transmission signal to the transmitter antenna and the two delay blocks;
2) when l is 0, during odd multiframes T1 and T2 are synchronously connected to the bottom branch, a sine wave (sin2 pi f)0t) multiplication with the output of the chaotic generator x (t), x (t) sin2 π f0t is transmitted as a transmission signal to the transmitter antenna and the two delay blocks;
3) when 1 ≦ l ≦ θ, T1 and T2 are synchronously connected to the top branch, and during the δ -th multiframe, the chaotic sequence transmitted in the first frame is used as a reference signal to carry the information symbol d1,δ,l. Since the time interval between two time delay blocks is theta frame, the chaotic sequence transmitted in frame 1 of the delta-th multiframe is used as a reference signal for carrying the information symbol d2,δ,l。
3. The method for SIMO-HPO-CDSK communication based on rayleigh fading channel as claimed in claim 1, wherein the receiver employs an Equal Gain Combiner (EGC) to obtain the performance gain in step S2.
4. The method for SIMO-HPO-CDSK communication based on rayleigh fading channel as claimed in claim 1, wherein the correlator outputs (y1, δ, l and y2, δ, l) in step S3 are explained by dividing into the following two conditions: calculating to obtain y when delta is odd number or even number1,δ,lAnd y2,δ,lThe conditional variance of (c).
5. The method for SIMO-HPO-CDSK communication based on rayleigh fading channel as claimed in claim 1, wherein all independent channels in step S4 satisfy the same rayleigh fading channel condition.
6. The SIMO-HPO-CDSK communication method based on Rayleigh fading channel as recited in claim 1,the parameters used in the SIMO-HPO-CDSK system in the step S5 are the same as those used in the conventional CDSK system by using 3-order Chebyshev mapping, that is, the parameters are xk+1＝4xk 3-3xkGenerating different chaotic sequences, the initial value x00.1, the average power gain of each Rayleigh fading channel is E [ h [ ]i 2]＝1。
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114826848A (en) * 2022-03-04 2022-07-29 重庆邮电大学 Communication method of enhanced high-efficiency short-parameter DCSK chaotic communication system
CN115134023A (en) * 2022-06-23 2022-09-30 杭州电子科技大学 Method and system for deriving average distortion theoretical value of uniformly quantized real-time communication system

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114826848A (en) * 2022-03-04 2022-07-29 重庆邮电大学 Communication method of enhanced high-efficiency short-parameter DCSK chaotic communication system
CN115134023A (en) * 2022-06-23 2022-09-30 杭州电子科技大学 Method and system for deriving average distortion theoretical value of uniformly quantized real-time communication system
CN115134023B (en) * 2022-06-23 2022-11-25 杭州电子科技大学 Method and system for deriving average distortion theoretical value of uniformly quantized real-time communication system

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