A low-complexity constellation design method for concentration shift keying

Abstract

The present invention discloses a low-complexity concentration shift keying constellation design method. The design method of the present invention takes into account that in the case of a channel accompanied by inter-symbol interference and signal-correlated noise, the transmitter randomly generates constellation points within the constraint of average energy, calculates the theoretical threshold corresponding to each constellation point after channel fading, and then uses the constellation points after fading and the corresponding threshold to calculate the symbol error rate, and finally finds the transmitter constellation point and threshold corresponding to the minimum symbol error rate among multiple symbol error rates, which is the optimal solution. The design method of the present invention not only achieves better symbol error rate performance than the traditional Uniform constellation design method and Square-root constellation design method, but can also be applied to the constellation point design of any order of the transmitter.

Description

Technical Field

[0001] The invention relates to the field of molecular communication, and in particular to a low-complexity concentration shift keying constellation design method. Background Art

[0002] With the rapid development of communication technology, traditional wired and wireless communication technologies have become the main means of communication in people's daily lives. However, communication technologies such as 5G are not suitable for application in some specific situations. For example, in underwater environments such as tunnels, pipelines or unpredictable oceans, electromagnetic wave communication signals will be severely attenuated. At this time, the use of electromagnetic wireless communication may be very inefficient. In addition, at extremely small sizes, such as communication between micro-nano devices and within the human body, electromagnetic communication will be limited by limitations such as the ratio of antenna size to electromagnetic signal wavelength, and acoustic wave communication will be limited by the size of the acoustic energy converter, making them unsuitable for small-scale scenarios, and the biocompatibility of these devices with the human body is not very good.

[0003] Molecular communication (MC) is a bio-inspired communication technology that uses chemical signals as information carriers. Molecular communication can not only achieve short-distance communication, such as inter- and intracellular communication at the micro-nanoscale, but also long-distance communication, such as social insects and sharks' perception of the smell of blood in the ocean. Compared with electromagnetic signals, the advantage of molecular communication is that it has low energy consumption characteristics, and very little energy is needed to generate and transmit signals. Although molecular communication cannot achieve the high data rate of wireless communication systems, the energy consumed for each piece of information they transmit is much less, which makes them suitable for ultra-low power applications that do not require high data rates. In addition, molecular communication has good biocompatibility. These characteristics make molecular communication an ideal choice for many niche communication applications.

[0004] Molecular communication has broad application prospects in many fields such as biomedicine, industry, military, and environment. The main purpose of communication is to transmit information, and in this process, ensuring the correctness of the transmitted information is a fundamental task. However, the premise for achieving the correct transmission of information in the application process is to improve the overall performance of the molecular communication system and reduce the symbol error rate in the communication process. Among them, modulation technology is a key part to achieve this goal. It can convert the transmitted information into a form suitable for transmission in the chemical process. Compared with traditional communication systems, the shortcomings of MC include serious inter-symbol interference (ISI) and signal-dependent noise. In this context, its advanced modulation design remains an open problem. At present, the modulation methods of MC mainly include category, concentration, type, time, space modulation and hybrid modulation. Similar to amplitude transfer keying in traditional communication systems, concentration shift keying (CSK) uses the concentration level of a single type of information molecule to transmit signals in MC systems. Among them, the simplest form of binary CSK is called on-off keying (OOK). In addition, molecular shift keying (MoSK) uses multiple types of messenger molecules to transmit information, which inevitably increases the design complexity of MC systems. In diffusion-based MC systems, ISI and signal-dependent noise are introduced due to the random diffusion process. To solve these problems, existing technologies include: signal processing technology at the MC receiver uses a model-based detector, uses the rising edge of the received signal as a differential metric to suppress interference, responds to the continuous received signal from the MC prototype, and achieves error-free performance, and a detector based on a time domain model to eliminate ISI and signal-dependent noise, converts signal-dependent noise into a useful signal that enhances the signal-to-noise ratio, uses a non-coherent detection method based on a time domain model to improve system error performance, and uses a low-complexity noise count suppression filter, which is superior to traditional denoising algorithms in terms of symbol error rate performance. In addition, some researchers have proposed a frequency domain equalizer that can significantly reduce ISI and signal-dependent noise at the same time. Compared with its time domain counterpart, its computational complexity is insensitive to the length of ISI. Therefore, in molecular communication systems, signal-correlated noise mainly affects the receiving signal. To improve the bit error rate performance of the system, researchers mainly focus on designing new indicators at the receiving end, such as the combination and arrangement of molecular types, without considering the constellation design of the system at the receiving end. Currently, the constellation design method at the transmitter end still uses the traditional Uniform constellation design method and Square-root constellation design method.

[0005] In summary, considering the signal-correlated noise, the modulation method designed at the receiver end in the traditional molecular communication system still needs to be improved to improve the symbol error rate, and the Uniform constellation design method and Square-root constellation design method based on the transmitter end cannot achieve better performance in improving the system symbol error rate. Summary of the invention

[0006] In view of the problems existing in the prior art, the purpose of the present invention is to provide a low-complexity density shift keying constellation design method. The present invention takes into account the influence of inter-symbol interference and signal-correlated noise, and provides a new design of constellation points.

[0007] The purpose of the present invention is achieved by the following technical solutions:

[0008] A low-complexity concentration shift keying constellation design method comprises the following steps:

[0009] Step 1: Establish a system model diagram, wherein the system model diagram consists of a point source transmitter and a spherical receiver, and the messenger molecules can freely enter and exit the spherical receiver;

[0010] Step 2: Calculate the channel impulse response of the spherical receiver and obtain the channel gain;

[0011] Step 3: Obtain a system model of the molecular receiving signal that takes into account both inter-symbol interference and signal correlation noise;

[0012] Step 4: approximate the ISI as statistical ISI and obtain the molecular received signal at the spherical receiver;

[0013] Step 5: Get the arbitrary order of the constellation points of the point source transmitter in the form of a vector, and use maximum likelihood detection to judge the molecular receiving signal in step 4;

[0014] Step 6: Calculate the theoretical threshold of the constellation point;

[0015] Step 7: Calculate the symbol error rate of the system and approximate it using the Q function;

[0016] Step 8: Constrain the number of transmissions and average transmission energy of a single constellation point of the point source transmitter.

[0017] Furthermore, in step 1, the distance between the point source transmitter and the spherical receiver is denoted as d, and the radius of the spherical receiver is denoted as r.

[0018] Furthermore, in step 2, the calculation formula of the channel impulse response is:

[0019]

[0020] In the formula, is the volume of the spherical receiver, D is the diffusion coefficient of the messenger molecule, and t is the time;

[0021] The calculation formula of channel gain h(l) is:

[0022] h(l)=h(t p +lT s ),l=0,1,…,L, (2)

[0023] In the formula, represents the peak time, i.e. the sampling time; L is the length of the inter-symbol interference; T s is the symbol duration; l is the index of inter-symbol interference; h(t p +lT s ) is the channel gain of the lth intersymbol interference, which is equivalent to h(l).

[0024] Furthermore, in step 3, the system model of the molecule receiving the signal is z m =y n,m +n m , where z m For molecules to receive signals, y n,m To transmit the signal, n m is the signal-dependent noise; and the signal at the spherical receiver includes the desired signal, inter-symbol interference and signal-dependent noise. Therefore, the system model of the molecular receiving signal is rewritten as:

[0025]

[0026] In the formula, x n,m is the number of molecules transmitted by the mth symbol, m = {1, 2, ...}, n∈S, where S = {1, 2, ..., n, ..., 2 N}, N is the number of bits per symbol, x n,m-l is the number of crosstalk molecules generated by the mlth symbol, is the total inter-symbol interference received by the mth symbol; n m It obeys Gaussian distribution, that is:

[0027]

[0028] Furthermore, in step 4, the statistical inter-symbol interference is expressed as:

[0029]

[0030] The molecular reception signal at the spherical receiver is calculated as:

[0031] z m =x n,m h(l)| l＝0 +x ISI +n m (6)

[0032] Furthermore, in step 5, the arbitrary order of the constellation points of the point source transmitter is expressed in the form of a vector:

[0033]

[0034] The judgment is made by the following formula, the symbol x n,m It is expressed as:

[0035]

[0036] In the formula, p(z m |x n,m ,x ISI ) is the probability density function, expressed as:

[0037]

[0038] Furthermore, in step 6, the theoretical threshold of the constellation point is the intersection point of adjacent constellation points, which is obtained by taking the logarithm of the probability density function and then obtaining the relationship between the number of molecules of each constellation point and the threshold, as follows:

[0039]

[0040] In the formula, Finally, the relationship is solved and expressed as:

[0041]

[0042] An arbitrary order of theoretical thresholds of constellation points can be expressed in vector form as:

[0043] τ=[τ1,…,τ n ,…,τ 2N-1 ]. (12)

[0044] Furthermore, in step 7, the symbol error rate is obtained by integrating the probability density function and then obtaining the probability of each symbol being correctly detected, which is expressed as:

[0045]

[0046] Using the Q function for approximation, it can be expressed as:

[0047]

[0048] Furthermore, in step eight, the constraint is expressed as:

[0049]

[0050] E=E(x), (16)

[0051] In the formula, represents the set of positive integers, is the expectation operator, E is the average transmitted energy, and x is the representation of the constellation points of the point source transmitter in an arbitrary order as a vector.

[0052] The beneficial effects of the present invention are:

[0053] 1. The design method of the present invention takes the optimization of the transmit constellation points and the theoretical thresholds of the constellation points on the transmitter side as the design goal, and finds the optimal transmitter-side constellation points and thresholds by minimizing the symbol error rate of the system, thereby achieving better symbol error rate performance than the traditional uniform constellation design method and square-root constellation design method.

[0054] 2. The design method of the present invention can be applied to the constellation point design of any order of transmitter end. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a system model diagram of the design method of the present invention.

[0056] Figure 2 It is a flow chart of the design method of the present invention.

[0057] Figure 3 4-order constellation design diagrams of the traditional Uniform constellation design method and the design method of the present invention under the same channel condition.

[0058] Figure 4 Graphs showing the eighth-order constellation design of the traditional Uniform constellation design method and the design method of the present invention under the same channel condition.

[0059] Figure 5 Figure 3 is a graph showing the relationship between the theoretical symbol error rate and the simulated symbol error rate of the fourth-order constellation point under channel conditions of different symbol durations and average energies.

[0060] Figure 6 The figure is a comparison diagram of symbol error rates of the traditional uniform design method, the square-root design method and the design method of the present invention for fourth-order constellation points under different spherical receiver radii and channel conditions of average energy.

[0061] Figure 7 Figure 3 is a graph showing the relationship between the theoretical symbol error rate and the simulated symbol error rate of the eighth-order constellation point under channel conditions of different symbol durations and average energies.

[0062] Figure 8The figure is a comparison diagram of symbol error rates of the traditional uniform design method, the square-root design method and the design method of the present invention for the eighth-order constellation point under the channel conditions of different spherical receiver radii and average energies. DETAILED DESCRIPTION

[0063] The specific embodiments of the present invention are further described below in conjunction with the accompanying drawings. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0064] Example:

[0065] A low-complexity concentration shift keying constellation design method comprises the following steps:

[0066] Step 1: Establish a system model diagram, wherein the system model diagram consists of a point source transmitter and a spherical receiver, and the messenger molecules can freely enter and exit the spherical receiver;

[0067] like Figure 1 As shown, the distance between the point source transmitter and the spherical receiver is denoted as d, and the radius of the spherical receiver is denoted as r.

[0068] Step 2: Calculate the channel impulse response (CIR) of the spherical receiver and obtain the channel gain;

[0069] The calculation formula of the channel impulse response is:

[0070]

[0071] In the formula, is the volume of the spherical receiver, D is the diffusion coefficient of the messenger molecule, and t is the time;

[0072] The calculation formula of channel gain h(l) is:

[0073] h(l)=h(t p +lT s ),l=0,1,…,L, (2)

[0074] In the formula, represents the peak time, i.e. the sampling time; L is the length of the inter-symbol interference; T s is the symbol duration; l is the index of inter-symbol interference; h(t p +lT s ) is the channel gain of the lth intersymbol interference, which is equivalent to h(l).

[0075] Step 3: Obtain a system model of the molecular receiving signal that takes into account both inter-symbol interference and signal correlation noise;

[0076] The system model of molecules receiving signals is z m =y n,m +n m , where z m For molecules to receive signals, y n,m To transmit the signal, n m is the signal-dependent noise; and the signal at the spherical receiver includes the desired signal, inter-symbol interference and signal-dependent noise. Therefore, the system model of the molecular receiving signal is rewritten as:

[0077]

[0078] In the formula, x n,m is the number of molecules transmitted by the mth symbol, m = {1, 2, ...}, n∈S, where S = {1, 2, ..., n, ..., 2 N}, N is the number of bits per symbol, x n,m-l is the number of crosstalk molecules generated by the mlth symbol, is the total inter-symbol interference received by the mth symbol; n m It obeys Gaussian distribution, that is:

[0079]

[0080] Step 4: approximate the ISI as statistical ISI and obtain the molecular received signal at the spherical receiver;

[0081] Statistical intersymbol interference is expressed as:

[0082]

[0083] The molecular reception signal at the spherical receiver is calculated as:

[0084] z m =x n,m h(l)| l＝0 +x ISI +n m (6)

[0085] Step 5: Get the arbitrary order of the constellation points of the point source transmitter in the form of a vector, and use maximum likelihood detection (MLD) to judge the molecular receiving signal in step 4;

[0086] The arbitrary order of the constellation points of a point source transmitter is represented as a vector:

[0087]

[0088] The judgment is made by the following formula, the symbol x n,m It is expressed as:

[0089]

[0090] In the formula, p(z m |x n,m ,x ISI ) is the probability density function, expressed as:

[0091]

[0092] Step 6: Calculate the theoretical threshold of the constellation point;

[0093] The theoretical threshold of a constellation point is the intersection of adjacent constellation points. The relationship between the number of molecules of each constellation point and the threshold is obtained by taking the logarithm of the probability density function, as follows:

[0094]

[0095] In the formula, Finally, the relationship is solved and expressed as:

[0096]

[0097] An arbitrary order of theoretical thresholds of constellation points can be expressed in vector form as:

[0098]

[0099] Step 7: Calculate the symbol error rate of the system and approximate it using the Q function;

[0100] The symbol error rate is obtained by integrating the probability density function and then obtaining the probability of each symbol being correctly detected, expressed as:

[0101]

[0102] In order to facilitate calculation, the Q function is used for approximation, which is expressed as:

[0103]

[0104] Step 8: Constrain the number of transmissions and average transmission energy of a single constellation point of the point source transmitter.

[0105] The constraints are expressed as:

[0106]

[0107] E=E(x), (16)

[0108] In the formula, represents the set of positive integers, is the expectation operator, E is the average transmitted energy, and x is the representation of the constellation points of the point source transmitter in an arbitrary order as a vector.

[0109] against Figure 1 Analysis:

[0110] The system model diagram of the design method of the present invention is composed of a point source transmitter and a spherical receiver, the distance between the point source transmitter and the spherical receiver is denoted as d, and the radius of the spherical receiver is denoted as r.

[0111] against Figure 2 Analysis:

[0112] The flowchart of the design method of the present invention is as follows: considering the case where the channel is accompanied by inter-symbol interference and signal-correlated noise, the transmitter randomly generates constellation points under the constraint of average energy, calculates the theoretical threshold corresponding to each constellation point after the channel fades, and then calculates the symbol error rate using the constellation point after fading and the corresponding threshold, and finally finds the transmitter constellation point and threshold corresponding to the minimum symbol error rate among multiple symbol error rates. The transmitter constellation point and threshold at this time are the optimal solution.

[0113] against Figure 3 Analysis:

[0114] Figure 2 is a fourth-order constellation design diagram of the traditional uniform constellation design method and the design method of the present invention under the same channel condition. It is easy to observe that the overlapping parts of the fourth-order constellation points designed by the traditional uniform constellation design method are more and more obvious than those of the design method of the present invention, and it can be intuitively seen that the design method of the present invention is superior to the design of the fourth-order constellation points.

[0115] against Figure 4 Analysis:

[0116] Figure 2 is an eighth-order constellation design diagram of the conventional uniform constellation design method and the design method of the present invention under the same channel conditions. It is easy to observe that the overlapping parts of the constellation points designed by the conventional uniform constellation design method increase with the increase of the order. The higher the order, the more overlapping parts. However, no overlap is found between the constellation points designed by the design method of the present invention, indicating that the design method of the present invention is suitable for the design of high-order constellation points and has good bit error performance.

[0117] against Figure 5 Analysis:

[0118] The figure is a relationship diagram between the theoretical symbol error rate and the simulated symbol error rate of the fourth-order constellation point under the channel conditions of different symbol durations and average energies. It is easy to observe that when the symbol duration is the same, the theoretical symbol error rate and the simulated symbol error rate basically overlap, which shows the correctness of the design method of the present invention. When the average energy and symbol duration continue to increase, the symbol error rate of the system also decreases, which shows that the change of symbol duration and average energy plays a decisive role in improving the system symbol error rate performance.

[0119] against Figure 6 Analysis:

[0120] The figure is a symbol error rate comparison chart of the traditional uniform design method, square-root design method and the design method of the present invention for the fourth-order constellation point under the channel conditions of different spherical receiver radius and average energy. It is easy to observe that when the receiver radius r and the symbol duration are constant, the symbol error performance of all design methods also improves with the increase of energy; when the receiver radius r increases and the average energy and symbol duration are constant, the symbol error rate performance of all design methods is improved; compared with the traditional uniform design method and square-root design method, the symbol error performance of the design method of the present invention is undoubtedly the best, and its advantage in code error performance will become more obvious with the increase of the receiver radius and average energy.

[0121] against Figure 7 Analysis:

[0122] The figure shows the relationship between the theoretical symbol error rate and the simulated symbol error rate of the eighth-order constellation point under different channel conditions of symbol duration and average energy. It is easy to observe that, similar to the fourth-order case, the theoretical and simulated symbol error rates are basically the same and the symbol error rate decreases with the increase of symbol duration and average energy. The performance of the theoretical and simulated symbol error rates does not differ due to the increase of constellation points, which further verifies that Figure 3 The design method of the present invention can be applied to the design of high-order constellation points.

[0123] against Figure 8 Analysis:

[0124] The figure is a comparison of the symbol error rates of the conventional uniform design method, the square-root design method and the design method of the present invention for the eighth-order constellation point under the channel conditions of different spherical receiver radii and average energies. It is easy to observe that Figure 6The conclusions are basically consistent, and the optimal symbol error rate performance of the design method of the present invention is not affected by the increase in constellation points. However, it can be seen from the figure that the symbol error rate performance of the traditional Uniform design method and the Square-root design method under the eighth-order constellation point design will change with the increase of average energy, which confirms that the design method of the present invention can always maintain its optimality under any channel conditions.

[0125] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A low-complexity concentration shift keying constellation design method, characterized in that: The following steps are involved: Step 1: Establish a system model diagram, wherein the system model diagram consists of a point source transmitter and a spherical receiver, and the messenger molecules can freely enter and exit the spherical receiver; Step 2: Calculate the channel impulse response of the spherical receiver and obtain the channel gain; Step 3: Obtain a system model of the molecular receiving signal that takes into account both inter-symbol interference and signal correlation noise; Step 4: approximate the ISI as statistical ISI and obtain the molecular received signal at the spherical receiver; Step 5: Get the arbitrary order of the constellation points of the point source transmitter in the form of a vector, and use maximum likelihood detection to judge the molecular receiving signal in step 4; Step 6: Calculate the theoretical threshold of the constellation point; Step 7: Calculate the symbol error rate of the system and approximate it using the Q function; Step 8: Constrain the number of transmissions and average transmission energy of a single constellation point of the point source transmitter.

2. A low-complexity concentration shift keying constellation design method according to claim 1, characterized in that: In the step 1, the distance between the point source transmitter and the spherical receiver is denoted as d, and the radius of the spherical receiver is denoted as r.

3. A low-complexity concentration shift keying constellation design method according to claim 2, characterized in that: In the step 2, the calculation formula of the channel impulse response is: In the formula, is the volume of the spherical receiver, D is the diffusion coefficient of the messenger molecule, and t is the time; The calculation formula of channel gain h(l) is: h(l)=h(t p +lT s ),l=0,1,…,L, (2) In the formula, Indicates the peak time, i.e., the sampling time; L is the length of the inter-symbol interference; T s is the symbol duration; l is the index of inter-symbol interference; h(t p +lT s ) is the channel gain of the lth intersymbol interference, which is equivalent to h(l).

4. A low-complexity concentration shift keying constellation design method according to claim 3, characterized in that: In step 3, the system model of the molecule receiving the signal is z m =y n,m +n m , where z m For molecules to receive signals, y n,m To transmit the signal, n m is the signal-dependent noise; and the signal at the spherical receiver includes the desired signal, inter-symbol interference and signal-dependent noise. Therefore, the system model of the molecular receiving signal is rewritten as: In the formula, x n,m is the number of molecules transmitted by the mth symbol, in N is the number of bits per symbol, x n,m-l is the number of crosstalk molecules generated by the mlth symbol, is the total inter-symbol interference received by the mth symbol; n m It obeys Gaussian distribution, that is:

5. A low-complexity concentration shift keying constellation design method according to claim 4, characterized in that: In step 4, the statistical inter-symbol interference is expressed as: The molecular reception signal at the spherical receiver is calculated as: z m =x n,m h(l)| l＝0 +x ISI +n m 。 (6) 6. A low-complexity concentration shift keying constellation design method according to claim 5, characterized in that: In step 5, the arbitrary order of the constellation points of the point source transmitter is expressed in the form of a vector: The judgment is made by the following formula, the symbol x n,m It is expressed as: In the formula, p(z m |x n,m ,x ISI ) is the probability density function, expressed as:

7. A low-complexity concentration shift keying constellation design method according to claim 6, characterized in that: In step 6, the theoretical threshold of the constellation point is the intersection of adjacent constellation points, which is obtained by taking the logarithm of the probability density function and then obtaining the relationship between the number of molecules of each constellation point and the threshold, as follows: In the formula, Finally, the relationship is solved and expressed as: An arbitrary order of theoretical thresholds of constellation points can be expressed in vector form as:

8. The low-complexity concentration shift keying constellation design method according to claim 7, characterized in that: In step 7, the symbol error rate is obtained by integrating the probability density function and then obtaining the probability of each symbol being correctly detected, which is expressed as: Using the Q function for approximation, it can be expressed as:

9. A low-complexity concentration shift keying constellation design method according to claim 8, characterized in that: In step eight, the constraint is expressed as: E=E(x), (16) In the formula, represents the set of positive integers, is the expectation operator, E is the average transmitted energy, and x is the representation of the constellation points of the point source transmitter in an arbitrary order as a vector.

Images