Log-likelihood ratio calculation method for PPM-SNSPD communication system

Abstract

The application discloses a log-likelihood ratio calculation method of a PPM-SNSPD communication system and relates to the technical field of deep space optical communication and communication receiver algorithm, and aims to solve the problem of low receiving sensitivity of the PPM-SNSPD system. The method comprises the following steps: constructing a SNSPD detection PPM symbol detection model and a mathematical model of a PPM-SNSPD channel; recording the light count vector of each time slot of each nanowire in the SNSPD detector; analyzing the PPM symbol detection state according to the light count vector; for each nanowire, calculating the log-likelihood ratio of the channel by using the light count vector and the symbol detection state; and adding the channel log-likelihood ratios of each nanowire to obtain the log-likelihood ratio of the entire SNSPD detector. The application considers the dead time characteristics of the SNSPD and the channel memory effect, more accurately describes the actual channel condition, and improves the receiving sensitivity and reliability of the communication link.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of deep space optical communication and communication receiver algorithm, and particularly relates to a log-likelihood ratio calculation method of a PPM-SNSPD communication system. BACKGROUND

[0002] With the deepening of deep space exploration activities, the requirements for communication systems are also getting higher and higher. Due to the long distance and large channel loss, deep space communication faces many challenges such as power limitation. In the deep space optical communication system, in order to improve the peak optical power and enhance the anti-interference ability, pulse position modulation (PPM) is usually used to encode the optical signal. PPM maps digital information to the position of a series of optical pulses, and the receiving end determines the transmitted symbol by detecting the pulse position. M-ary PPM (M-PPM) modulation divides each symbol period into M time slots, and only one time slot carries an optical pulse, and the remaining time slots are empty. This sparse modulation method can obtain higher peak power under the condition of limited average power.

[0003] At the receiving end of the deep space optical communication system, single-photon detection technology is the key to realize high-sensitivity photon-level detection. The superconducting nanowire single-photon detector (SNSPD) has been widely used in ground receiving systems for deep space optical communication due to its excellent detection efficiency, low dark count and high time resolution.

[0004] Therefore, the laser communication system (referred to as PPM-SNSPD communication system) that the transmitting end uses PPM to generate optical signals and the receiving end uses SNSPD detectors to receive optical signals becomes the preferred system for deep space exploration. This communication system has been verified in existing international deep space laser communication projects (in 2013, NASA's Lunar Laser Communication Demonstration (LLCD) project, and in October 2023, NASA launched the Psyche satellite to carry out asteroid exploration mission (DSOC project)).

[0005] For the PPM-SNSPD communication system, modeling the photon detection process and accurately calculating the log-likelihood ratio (LLR) required for decoding are crucial for optimizing the performance of the communication system. Traditional SNSPD models are mostly based on time slot level, and it is difficult to reflect the difference in optical power distribution in PPM signals.

[0006] CN 108781129 A discloses that the LLR calculation unit includes: a range detection unit that detects which range of a plurality of ranges decided based on a boundary value in the modulo operation the received signal after the modulo operation is in; a coefficient decision unit that decides a coefficient used for calculation of a log likelihood ratio of a most significant bit in quadrature phase amplitude modulation of the received signal after the modulo operation based on a detection result obtained by the range detection unit; and an LLR calculation unit that calculates the log likelihood ratio of the most significant bit using the received signal after the modulo operation and the coefficient.

[0007] CN 101237247 B discloses the present invention relates to a method for deriving bit log likelihood ratios from symbol log likelihood ratios, belonging to the field of communication technology. In an OFDM communication system, a receiver is provided, which is composed of a forward error correction inner code device, or a forward error correction outer code device. Irrespective of the forward error correction inner code device or the forward error correction outer code device, an improved calculation method from symbol log likelihood ratios to bit log likelihood ratios is included. The steps of the method are: providing two simplified parameters; using the two simplified parameters in the calculation of the bit log likelihood ratios from the already obtained symbol log likelihood ratios, and only having addition and subtraction operations.

[0008] CN 103081426 B provides a method and system for calculating a likelihood metric for a demodulated complex coordinate data point, and dynamically scaling the likelihood metric as a function of channel statistics, and decoding the data point based on the scaled likelihood metric. The likelihood metric can be calculated with respect to all points or a subset of points of a reference constellation, such as a subset of one or more nearest constellation points, and can be scaled as a function of channel frequency response variance among multiple carriers, such as carriers of an OFDM signal, and / or as a function of channel impulse response variance.

[0009] The above three patents are not applicable to PPM-SNSPD optical communication systems, especially deep space laser communication systems. Most of the existing patents are for systems such as OFDM, and do not consider the characteristics of deep space photon-poor channels, and are no longer applicable to deep space optical links. SUMMARY

[0010] The present application aims to solve the problem that the log-likelihood ratio (LLR) calculation method of the PPM-SNSPD communication system in the existing deep space laser communication system is based on the ideal Poisson channel, without considering the dead time of the SNSPD and the memory characteristics of the channel, resulting in low receiving sensitivity of the PPM-SNSPD system, which cannot meet the demand of deep space laser communication, and proposes a log-likelihood ratio calculation method for a PPM-SNSPD communication system. The method considers the dead time effect of the SNSPD, defines five symbol detection states based on the working characteristics of the SNSPD, and derives the corresponding LLR calculation formula, and the results show that the receiving sensitivity of the system is greatly improved.

[0011] The present application proposes a log-likelihood ratio calculation method for a PPM-SNSPD communication system, comprising the following steps:

[0012] S1, the receiver uses a superconducting nanowire single-photon detector SNSPD to detect photons, constructs a SNSPD detection pulse position modulation PPM symbol detection model, and constructs a mathematical model of the PPM-SNSPD channel;

[0013] S2, record the light count vector of each time slot in each nanowire of the SNSPD detector;

[0014] S3, analyze the pulse position modulation PPM symbol detection state according to the light count vector of the SNSPD detector;

[0015] S4, for each nanowire, use the light count vector and the symbol detection state to calculate the log-likelihood ratio LLR of the nanowire single channel;

[0016] S5, add the log-likelihood ratio of each nanowire single channel to obtain the log-likelihood ratio of the entire SNSPD detector.

[0017] Further,

[0018] According to the Poisson distribution, without considering the dead time, the probability that the number of photons arriving at the detector in a single time slot T s is n1 is:

[0019]

[0020] Due to the influence of the dead time, the relationship between the number of detected photons y in a single time slot and the number of photons n1 arriving in a single time slot is:

[0021]

[0022] Therefore, in the state considering the dead time, the count probability of detecting y photons of photons in T s follows the Bernoulli distribution:

[0023]

[0024] where P poi (0, μT s ) is the probability that no photon arrives at the detector in a time slot, μ is the average number of photons arriving at the detector per second, T s is the width of a time slot.

[0025] Further, for a nanowire in the SNSPD detector, in a time slot, and on the premise that the nanowire is not in the dead time when the time slot starts, p 00 , p 01 , p 10 , p 11 are defined as follows:

[0026] p 00 : the probability that the nanowire does not detect a photon when the sending end does not send a pulse;

[0027] p 01 : the probability that the nanowire does not detect a photon when the sending end sends a pulse;

[0028] p 10 : the probability that the nanowire detects a photon when the sending end does not send a pulse;

[0029] p 11 : the probability that the nanowire detects a photon when the sending end sends a pulse;

[0030] The detection matrix is obtained as follows: The calculation formula is as follows:

[0031]

[0032] where n s and n b represent the average number of signal photons and noise photons arriving at the nanowire in a time slot, P Ber is the Bernoulli distribution of the counting probability of the photons.

[0033] Further, the S3 comprises:

[0034] The light counting vector y = [y0, y1,..., y M-1 ] of each time slot of each nanowire in the SNSPD detector is recorded, the received signal y is demodulated to obtain a soft decision estimation value defined as when the sending symbol is x i , the conditional probability of receiving y is P(y|x i ), and a more accurate soft decision estimation value P(y|x i, S),

[0035] where y i is the photon count of the i-th time slot of the symbol, and S refers to the symbol detection state.

[0036] Further, the S4 comprises:

[0037] For a single nanowire in the SNSPD detector, y j represents that the nanowire detects a photon in the j-th time slot of the symbol period, where y j = -1 represents that no photon is detected in the symbol period, and the calculation method of the single-channel log-likelihood ratio (LLR) of the nanowire in different symbol detection states is as follows:

[0038] When the nanowire is in the active state D0D, the symbol sent by the sending end is x i Under the condition that a photon is detected at time j, the single-channel LLR calculation formula is:

[0039]

[0040] where D0D represents that the nanowire is in the active state at the beginning of the symbol period and a photon is detected thereafter, i represents the time slot of the sending pulse, p 00 represents the probability that the nanowire does not detect a photon when the sending end does not send a pulse; p 01 represents the probability that the nanowire does not detect a photon when the sending end sends a pulse; p 10 represents the probability that the nanowire detects a photon when the sending end does not send a pulse; and p 11 represents the probability that the nanowire detects a photon when the sending end sends a pulse.

[0041] Optionally, the S4 further comprises:

[0042] When the nanowire is in the dead time state DND, the symbol sent is x i , and the single-channel LLR calculation formula when a photon is detected at time j is:

[0043]

[0044] where DND represents that the nanowire is in the dead time at the beginning of the symbol period, is in the active state at the h-th time slot, and a photon is detected thereafter, y j represents that the nanowire detects a photon in the j-th time slot of the symbol period, i represents the time slot of the sending pulse, p 00 represents the probability that the nanowire does not detect a photon when the sending end does not send a pulse; p 01 represents the probability that the nanowire does not detect a photon when the sending end sends a pulse; p 10P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p 11 P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p

[0045] Optionally, the S4 further comprises:

[0046] When the nanowire is in the state D0E, the transmitted symbol is x i The single-channel LLR calculation formula for detecting a photon at the jth time is:

[0047]

[0048] P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p j P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p 00 P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p 01 P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p 10 P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p 11 P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p

[0049] Optionally, the S4 further comprises:

[0050] When the nanowire is in the state D0E, the transmitted symbol is x i The single-channel LLR calculation formula for detecting a photon at the jth time is:

[0051]

[0052] P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p j P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p j P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p 00 P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p 01 P (D0E | x, y) represents the probability that the nanowire detects a photon when the transmitting end does not send a pulse; p

[0053] Optionally, the S4 further comprises:

[0054] When the nanowire is in the state D0E, the transmitted symbol is x i The single-channel LLR calculation formula for detecting a photon at the jth time is:

[0055] ln[Pr{y j＝-1 |x i ,D i}]=0;

[0056] where Di represents that the nanowire is in an undetectable state in the entire symbol period; i=1,...N-1, N represents a dead time factor, y j represents that the nanowire detects a photon in the jth time slot of the symbol period, y j＝-1 represents that no photon is detected in the symbol period.

[0057] Further, the log-likelihood ratio of the entire SNSPD detector in the S5 specifically comprises:

[0058]

[0059] where ln[Pr{y (l) |x i ,S (l)}] represents the single-channel log-likelihood ratio of the lth nanowire, y (l) represents the photon detection result of the nanowire, S (l) represents the symbol detection state of the nanowire, and the processes of different nanowires detecting photons are independent of each other.

[0060] Compared with the prior art, the beneficial effects of the present application relative to the prior art are:

[0061] The LLR calculation method based on the PPM-SNSPD communication system proposed in the present application can consider the influence of the dead time spanning multiple symbol periods, can extend the model to a high-order Markov process, introduce longer state memory, and is expected to obtain more accurate channel description, but at the same time, the calculation complexity is increased. It is necessary to balance the modeling accuracy and the implementation difficulty. According to the method provided in the present application, the present application proposes a new type of log-likelihood ratio (LLR) calculation method for the PPM-SNSPD communication system, for the PPM-SNSPD communication system used in deep space laser communication. Compared with the LLR calculation based on the ideal Poisson channel, the method considers the dead time characteristics of the SNSPD and the channel memory effect, can more accurately describe the actual channel condition, and improves the receiving sensitivity and reliability of the communication link. BRIEF DESCRIPTION OF DRAWINGS

[0062] The drawings described herein are used to provide further understanding of the present application, and form a part of the present application. The illustrative embodiments of the present application and their descriptions serve to explain the present application, and do not constitute an improper limitation on the present application. In the drawings:

[0063] Figure 1A PPM-SNSPD communication system's log likelihood ratio calculation system block diagram of the present application;

[0064] Figure 2 A PPM-SNSPD communication system's log likelihood ratio calculation method flow chart of the present application;

[0065] Figure 3 A photon time slot detection state's state transition diagram of the present application;

[0066] Figure 4 A 16-PPM's symbol detection state diagram of the present application;

[0067] Figure 5 A symbol detection state's transition diagram of the present application;

[0068] Figure 6 A PPM-SNSPD communication system's LLR calculation's SCPPM encoding system's error rate diagram of the present application. DETAILED DESCRIPTION

[0069] In order to clearly describe the technical scheme of the embodiments of the present application, in the embodiments of the present application, the same items or similar items with basically the same function and role are distinguished by using "first", "second" and the like. For example, the first threshold and the second threshold are only used to distinguish different thresholds, and do not limit the order. Those skilled in the art can understand that "first", "second" and the like do not limit the quantity and execution order, and "first", "second" and the like do not necessarily mean different.

[0070] It should be noted that in the present application, "exemplary" or "for example" and the like are used to represent as an example, illustration or description. Any embodiment or design scheme described as "exemplary" or "for example" in the present application should not be interpreted as more preferred or more advantageous than other embodiments or design schemes. Rather, the use of "exemplary" or "for example" and the like is intended to present the relevant concept in a specific manner.

[0071] Figure 1It is a PPM-SNSPD communication system of the application. The system is a PPM-SNSPD-based communication system. The calculation of LLR plays a crucial role in decoding. First, LLR is a kind of soft information measurement, which not only provides the most likely value of the bit (hard decision), but also contains the reliability information, that is, the probability ratio of the time slot of the optical signal. This kind of soft information helps to improve the decoding performance. Secondly, in the cascaded coding system, LLR can be transmitted between different decoding modules as a medium for soft information exchange. The transmitting end of the system modulates the information into a PPM optical signal, which is detected by the SNSPD of the receiving end after channel transmission. Among them, the transmitting end of the system uses the driver to amplify the peak voltage after using SCPPM to encode the input data. The amplified electrical signal is converted into an optical signal using a modulator.

[0072] At the receiving end of the system, the SNSPD converts the optical signal into an electrical signal and generates a dead time after detecting a photon event. The received electrical signal is sampled by time slot, and the value of each time slot depends on whether a photon event occurs and whether the adjacent time slot is in the dead time. According to the sampling sequence and the parameters of the SNSPD (such as quantum efficiency, dark count rate and dead time), the probability of each time slot in the symbol being a signal time slot can be calculated, and the LLR can be obtained from the ratio. This LLR calculation method using dead time can simplify the hardware structure while ensuring performance, but the influence of dead time needs to be fully considered in system design and modeling.

[0073] The LLR calculation method of the application is applicable to a general system model of any channel coding scheme. The transmitting part can use any channel coding, and the receiver is changed to a decoder corresponding to the channel coding of the transmitting end. Preferably, SCPPM is a kind of encoding technology, which means that a special structure of SCC code is used for channel coding first, and then PPM coding is used for channel coding. Correspondingly, SCPPM decoding is also a decoding for the SCC code.

[0074] For the entire PPM-SNSPD communication system, the receiver uses SNSPD detectors (which can include one or more nanowires) to detect photons. PPM-SNSPD channel refers to a nanowire in the SNSPD detector. That is, an SNSPD detector using L nanowires corresponds to L parallel PPM-SNSPD channels, and the statistical properties (i.e. channel model) of these channels are the same.

[0075] Therefore, the total LLR of the entire SNSPD detector is obtained by adding the LLRs corresponding to all nanowires (single-channel LLR).

[0076] Figure 2A flow chart of a PPM-SNSPD detector log-likelihood ratio calculation method.

[0077] (1) Construct a SNSPD detection PPM symbol detection model, and construct a mathematical model of a PPM-SNSPD channel:

[0078] A superconducting nanowire single-photon detector (SNSPD) is a single-photon detector, which has the advantages of high detection efficiency and sensitivity, low noise, short dead time and short time jitter; due to the dead time (T d ) characteristics of the SNSPD, the detection behavior of the SNSPD has memory. In a deep space optical communication system, in order to improve the peak optical power and enhance the anti-interference ability, pulse position modulation (PPM) is widely used in deep space communication systems; the detection result of the current PPM symbol will affect the detection of the subsequent PPM symbol, and the memory of the detector needs to be considered to accurately establish a mathematical model of a PPM-SNSPD channel.

[0079] Each M-PPM symbol is composed of M time slots, given a time slot width Ts, the PPM symbol period is T sym = MT s ; in PPM modulation, only one time slot carries the optical power transmitted by the transmitter, which is called the pulse time slot; the remaining time slots are called noise time slots; the signal time slot is selected from the M time slots with equal probability.

[0080] Consider a simplified case where the dead time is N times the symbol period T sym : T d = NT sym = NMT s ; wherein N is a positive integer multiple of the dead time factor; that is, once the SNSPD detects a photon and enters the dead time, the following N-1 symbols will be completely erased, and the Nth subsequent symbol will be partially erased.

[0081] In view of the dead time characteristics of the SNSPD and the memory characteristics of the photon detection behavior, a finite state machine is used to model the PPM-SNSPD communication system, which describes the photon detection state from two angles: time slot detection state and symbol detection state, the former describes the detection behavior of any optical signal, and the latter describes the detection behavior of pulse position modulation (PPM) signal; the detection behavior is described by a state transition diagram as shown in Figure 3 .

[0082] Figure 3Fig. 1 is a state transition diagram of a photon time slot detection state according to the present application. In this model, each nanowire in the SNSPD detector has three possible time slot detection states, which are: waiting time slot, counting time slot and dead time time slot. The waiting time slot means that the nanowire is in an active state (capable of detecting photons) but no photons reach the nanowire. The counting time slot means that the nanowire is in an active state (capable of detecting photons) and photons reach the nanowire. The dead time time slot means that the nanowire is in a dead time (unable to detect photons)

[0083] First, when the nanowire is not in the dead time and no photons are detected, the time slot will remain in the waiting time slot state. When the temperature of the nanowire remains below 3 Kelvin, the energy of a single photon can destroy its local superconductivity. At this time, the bias current flowing through the nanowire generates a large amount of Joule heat, causing the non-superconducting region to rapidly expand, the resistance to rapidly rise, and a single-photon voltage pulse to be formed. This pulse can be used as a single-photon counting signal. The time slot in which the photon is detected is called the photon counting time slot. Then, once a photon is detected, the nanowire will be unable to detect new photons because it needs to wait for the bias circuit to completely discharge its accumulated charge, and at the same time the heat of the nanowire begins to be absorbed by the substrate. During this time, the nanowire cannot respond to the incident photons. This period of time in which the nanowire cannot detect photons is called the dead time, that is, the dead time time slot. When the dead time ends, the nanowire will transition to the waiting time slot state (the photon hits the nanowire after a certain waiting time) or the counting time slot state (the photon hits the nanowire immediately after the dead time ends). Figure 3 The dashed line (----) represents that no photons reach the nanowire (no photons are detected) in the next time slot; the dotted line (--.--.--.) represents that photons reach the nanowire (one photon is detected) in the next PPM time slot; and the solid line represents that the nanowire is always in the dead time in the next PPM time slot.

[0084] (2) Detection of pulse position modulation (PPM) signals

[0085] In the PPM-SNSPD communication system, since the intensity of the PPM signal is not constant, the instantaneous probability of photon hitting also changes according to whether the transmitter emits a pulse. However, the above time slot detection model cannot reflect these characteristics. The present application establishes a symbol-level detection model.

[0086] For ease of analysis, we use time slots as the minimum time unit to analyze the behavior of the nanowire in PPM symbol detection.

[0087] Figure 4A 16-PPM symbol detection state diagram of the present application. This diagram takes 16-PPM as an example, each nanowire has five symbol detection states (Di, D0E, D0D, DND, DNE). Among them, Di represents that the nanowire is in dead time during the entire M-PPM symbol, when N = 1, there is no such state, it is also called non-active symbol detection state; D0E represents that the nanowire is in active state at the beginning of the symbol period, and no photons arrive; D0D represents that the nanowire is in active state at the beginning of the symbol period, and photons arrive and are detected by the nanowire; DND represents that the nanowire is in dead time (dead time time slot) state at the beginning, and then recovers to active state in the symbol period, then photons arrive and produce light counts; DNE represents that the nanowire is in dead time state at the beginning, and then recovers to active state in the symbol period, and no photons arrive.

[0088] It should be emphasized that in the state name, i, 0 and N respectively represent the number of symbols that have been in dead time. The first time slot in the Di state comes from the ith symbol in the N symbols, and the first time slot in the DND or DNE state comes from the last symbol of the dead time. In summary, the above five symbol detection states describe the behavior of the nanowire in a symbol time. In addition, according to the initial state of the symbol period, the symbol detection states other than Di can be divided into: 1) fully active state (D0E and D0D): the nanowire is in active state at the beginning of the symbol period; 2) partially active state (DND and DNE): the nanowire is in dead time at the beginning, and then recovers to active state in the same symbol period.

[0089] According to the assumption of Poisson photon arrival, without considering the dead time, the probability of the number of photons n1 arriving at the detector in a single time slot T s is

[0090]

[0091] where μ is the average number of photons arriving at the detector per second.

[0092] Considering that T d = MNT s , at most one photon can be detected in a single time slot T s . Therefore, the relationship between the number of photons y detected in a time slot and the number of photons n1 arriving in a single time slot is:

[0093]

[0094] Therefore, in the state considering the dead time, the probability of detecting y photons by the photon in T s follows the Bernoulli distribution:

[0095]

[0096] where 1-P poi (0, μT s ) is the probability that at least one photon arrives at the detector in a time slot; P poi (0, μT s ) is the probability that no photon arrives at the detector in a time slot, μ is the average number of photons arriving at the detector per second, T s is the width of a time slot. n s is defined as the average number of photons from the pulse arriving in a time slot when the transmitter is transmitting a pulse. n b is defined as the average number of photons from the noise arriving in a time slot. A signal time slot has n s = n s + n b photons, and a non-signal time slot has n s = n b photons. Based on the results given in the equations, the probability that no photon is detected in a non-signal time slot can be expressed as p 00 = P Ber (0; n b ). By simple extension, the derivation of the detection matrix is

[0097]

[0098] where, for a nanowire, in a time slot, and provided that the nanowire is not in dead time at the beginning of the time slot, p 00 , p 01 , p 10 , and p 11 are defined as follows:

[0099] p 00 : the probability that the nanowire detects no photon when the transmitter is not transmitting a pulse;

[0100] p 01 : the probability that the nanowire detects no photon when the transmitter is transmitting a pulse;

[0101] p 10 : the probability that the nanowire detects a photon when the transmitter is not transmitting a pulse;

[0102] p 11 : the probability that the nanowire detects a photon when the transmitter is transmitting a pulse.

[0103] (3) Calculation of Channel Likelihood Ratio

[0104] Continuous serial concatenated pulse position modulation (SCPPM) is the coding standard recommended by CCSDS for deep space optical communication. It is composed of convolutional code, interleaver, accumulator and PPM encoder. At the receiving end, the SCPPM decoder inputs the log-likelihood ratio (LLR) of the received signal and outputs the soft decision estimate of the transmitted binary data. LLR is crucial for SCPPM to maintain good error correction performance at low optical power.

[0105] For an ideal Poisson channel, the vector y = [y0, y1,..., yN-1] represents the photon counting sequence of a PPM symbol period, where y M-1 is the photon count of the i-th time slot of the symbol, and the demodulated soft decision estimate of the received signal y is defined as i When the transmitted symbol is x i , the conditional probability of receiving y is P(y | x i ). Usually, the soft decision estimate is expressed in logarithmic form ln[Pr{y | x i}] and is called log-likelihood ratio (LLR). The formula for calculating the LLR of y under an ideal Poisson channel can be expressed as:

[0106]

[0107] where y i follows a Poisson distribution. In the above formula, the constant term C has no effect on the subsequent decoding results and can be omitted when calculating the LLR.

[0108] However, in an actual deep space laser communication system based on PPM-SNSPD, due to the influence of SNSPD dead time, its channel is not an ideal Poisson channel, but a partially Poisson channel with memory, i.e. the detection result of the current symbol will affect the detection of subsequent symbols. Using the LLR expression that does not conform to the actual channel will result in decoding performance loss. Therefore, we can obtain a more accurate soft decision estimate P(y | x i , S) by continuously tracking the detection state transition of each nanowire in the SNSPD detector, where the detection state S refers to the symbol detection state (Di, D0E, D0D, DND, DNE).

[0109] First, consider a single nanowire, and use y j to represent the detection of a photon by the nanowire in the j-th time slot of the symbol period, where y j＝-1 represents no detection of a photon in the symbol period. The detailed calculation method of the single-channel LLR ln[Pr{y | x i , S}] under different symbol detection states is as follows:

[0110] 1) D0D represents that the nanowire is in the active state at the beginning of the current symbol period and a photon is detected afterward. When the nanowire is in this state, the symbol sent by the sending end is x i The single-channel log-likelihood ratio of detecting a photon at time j under the condition that the symbol sent by the sending end is x

[0111]

[0112] where D0D represents that the nanowire is in the active state at the beginning of the current symbol period and a photon is detected afterward, i represents the time slot of the sending pulse, p 00 represents the probability that the nanowire does not detect a photon when the sending end does not send a pulse; p 01 represents the probability that the nanowire does not detect a photon when the sending end sends a pulse; p 10 represents the probability that the nanowire detects a photon when the sending end does not send a pulse; p 11 represents the probability that the nanowire detects a photon when the sending end sends a pulse.

[0113] 2) DND represents that the nanowire is in the dead time at the beginning of the symbol period and recovers the active state at the hth time slot and then detects a photon. In this state, the symbol sent by the sending end is x i The single-channel log-likelihood ratio of detecting a photon at time j is:

[0114]

[0115] where DND represents that the nanowire is in the dead time at the beginning of the symbol period, recovers the active state at the hth time slot, and then detects a photon, y j represents that the nanowire detects a photon at the jth time slot of the symbol period, i represents the time slot of the sending pulse, p 00 represents the probability that the nanowire does not detect a photon when the sending end does not send a pulse; p 01 represents the probability that the nanowire does not detect a photon when the sending end sends a pulse; p 10 represents the probability that the nanowire detects a photon when the sending end does not send a pulse; p 11 represents the probability that the nanowire detects a photon when the sending end sends a pulse.

[0116] 3) D0E represents that the nanowire is in the active state throughout the symbol period but does not detect a photon. When the nanowire is in this state, the symbol sent by the sending end is x i The single-channel log-likelihood ratio of not receiving a photon is:

[0117] ln[Pr{y j |x i , D0E}] = (M-1) ln(p 00)+ln(p 01 )

[0118] where D0Erepresents that the nanowire is active throughout the symbol period but no photon is detected, y j represents that the nanowire detects a photon at the jth time slot of the symbol period, i denotes the time slot in which the pulse is transmitted, p 00 represents the probability that the nanowire does not detect a photon when the transmitting end does not transmit a pulse; p 01 represents the probability that the nanowire does not detect a photon when the transmitting end transmits a pulse. 10 represents the probability that the nanowire detects a photon when the transmitting end does not transmit a pulse. 11 represents the probability that the nanowire detects a photon when the transmitting end transmits a pulse.

[0119] 4) DNE represents that the nanowire is in dead time at the beginning of the symbol period and recovers to the active state at the hth time slot. When the nanowire is in the DNE state, the symbol transmitted by the transmitting end is x i , and the single-channel log-likelihood ratio without receiving a photon is:

[0120]

[0121] where DNE represents that the nanowire is in dead time at the beginning of the symbol period and recovers to the active state at the hth time slot, y j represents that the nanowire detects a photon at the jth time slot of the symbol period, y j＝-1 represents that no photon is detected in the symbol period, i denotes the time slot in which the pulse is transmitted, p 00 represents the probability that the nanowire does not detect a photon when the transmitting end does not transmit a pulse; p 01 represents the probability that the nanowire does not detect a photon when the transmitting end transmits a pulse.

[0122] 5) Di represents that the nanowire is in an undetectable state throughout the symbol period, where i = 1,... N-1, and N represents a dead time factor. When the nanowire is in the Di state, the symbol transmitted by the transmitting end is x i , and the probability of not detecting a photon is ln

[0123] ln[Pr{y j＝-1 |x i , Di}] = 0.

[0124] where Di represents that the nanowire is in an undetectable state throughout the symbol period; i = 1,... N-1, and N represents a dead time factor, y j represents that the nanowire detects a photon at the jth time slot of the symbol period, y j＝-1No photon is detected in the symbol period.

[0125] For SNSPD detectors, we first calculate the single-channel LLR for each nanowire using the above method, where the single-channel LLR for the lth nanowire is denoted as ln[Pr{y (l) |x i , S (l)}], y (l) represents the photon detection result of the nanowire, S (l) represents the symbol detection state of the nanowire, and the photon detection processes of different nanowires are independent of each other. Then, the total LLR of the SNSPD detector can be calculated as:

[0126]

[0127] As analyzed above, the calculation steps of the total LLR of the SNSPD detector are as follows: 1) record the light count vector and the symbol detection state of each nanowire in each time slot of the SNSPD detector; 2) for each nanowire, calculate the single-channel LLR using its own light count vector and symbol detection state using the above formula; and 3) add the single-channel LLRs given by each nanowire to obtain the total LLR of the entire SNSPD detector.

[0128] Figure 5 Fig. 4 is a schematic diagram of a symbol detection state transition according to the present application, which is an auxiliary description for tracking the PPM detection state. Each box represents a state, and the arrow from state A to state B represents that if the detection state of the current PPM symbol is state A, then the symbol detection state of the next PPM will be state B under certain conditions. If there is no arrow between state A and state B, it means that the next state of state A will not be state B, and vice versa. The line type of the arrow represents different conditions. The dashed line (----) represents that the SNSPD does not detect a photon in the next PPM symbol; the dotted dashed line (---.

[0129] ---.) represents that the SNSPD detects a photon in the next PPM symbol; and the solid line represents that the SNSPD is in the dead time all the time in the next PPM symbol.

[0130] Figure 6 Fig. 5 is an error rate diagram of an SCPPM encoding system for LLR calculation of a PPM-SNSPD communication system according to the present application. In this figure, the BER performance of the log-likelihood ratio based on the Poisson channel model and the log-likelihood ratio based on the PPM-SNSPD communication system model (hereinafter referred to as Poisson LLR and dead time LLR, respectively) after SCPPM decoding under different PPM orders is simulated and analyzed. In the figure, the horizontal axis is the normalized average optical power (P avg ), which is defined as Pavg = n s / M.

[0131] The simulation conditions are as follows: the symbol period remains unchanged, while the slot width decreases as the modulation order increases; the dead time factor N is set to 4; the noise intensity n b is equal to 9 / M. The simulation results show that, compared with the Poisson LLR, the dead time LLR algorithm provides higher communication sensitivity. For example, in the case of 16-PPM, SCPPM decoding using the Poisson LLR decreases to a bit error rate of 10 avg at P -5 = 1.2 dB, while SCPPM decoding using the dead time LLR can decrease to a bit error rate of 10 avg at P -5 = -1 dB, i.e., a performance gain of 2.2 dB is provided. In addition, in the case of 16-PPM, it can be observed that, when the Poisson LLR is used, the bit error rate suddenly rises at P avg = 3 dB or so, and the bit error rate then continuously increases to 10 -2 below. The bit error rate performance using the dead time LLR does not have the case of bit error rate deterioration. This gain is due to the new type of LLR, which can accurately reflect the actual channel conditions and provide supplementary channel decoding information.

[0132] The LLR calculation algorithm based on the PPM-SNSPD communication system proposed in the present application can take into account the influence of the dead time spanning multiple symbol periods, can extend the model to a high-order Markov process, introduce longer state memory, and is expected to obtain more accurate channel description, but at the same time will increase the calculation complexity. The modeling accuracy and implementation difficulty need to be balanced. According to the content provided by the present application, the present application proposes a new type of log-likelihood ratio (LLR) calculation method for a communication system, for the PPM-SNSPD communication system used in deep space laser communication. Compared with the LLR calculation based on the ideal Poisson channel, this method takes into account the dead time characteristics of the SNSPD and the channel memory effect, can more accurately describe the actual channel conditions, and improves the receiving sensitivity and reliability of the communication link.

[0133] All related contents of each step involved in the above method embodiment can be cited to the function description of the corresponding function module, which will not be repeated here.

[0134] In the above embodiments, all or part can be implemented by software, hardware, firmware or any combination thereof. When implemented by software, all or part can be implemented in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer programs or instructions are loaded on a computer and executed, all or part of the processes or functions described in the embodiments of the present application are performed. The computer can be a general purpose computer, a special purpose computer, a computer network, a terminal, a user equipment or other programmable apparatus. The computer programs or instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, the computer programs or instructions can be transferred from one website site, computer, server or data center to another website site, computer, server or data center through wired or wireless manner. The computer readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center and the like integrated with one or more available media. The available media can be a magnetic medium, such as a floppy disk, a hard disk, a magnetic tape; an optical medium, such as a digital video disc (digital video disc, DVD); and a semiconductor medium, such as a solid state drive (solid state drive, SSD).

[0135] Although the present application has been described in connection with various embodiments thereof, it will be understood that other variations and modifications of the disclosed embodiments can be made by those skilled in the art upon reading the description of the application set forth above. In the claims, the word "comprising" does not exclude other components or steps not mentioned in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. A single processor or other unit can fulfill the functions of several items recited in the claims. Several measures can be combined into one measure. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0136] Although the present application has been described in connection with specific features thereof, it will be understood that various modifications and variations can be made by those skilled in the art upon reading the description of the application set forth above. Accordingly, the description and drawings set forth above are illustrative only and are not intended to limit the scope of the application as defined in the claims. It will be apparent to those skilled in the art that various modifications and variations can be made in the present application without departing from the spirit and scope of the application. Thus, it is intended that the present application embrace all such modifications and variations as fall within the scope of the appended claims and their equivalents. Obviously, many modifications and variations of the present application are possible in light of its teachings. It is, therefore, to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.

Claims

1. A method for calculating the log-likelihood ratio of a PPM-SNSPD communication system, characterized in that, The method comprises the following steps: S1, a receiver uses a superconducting nanowire single-photon detector (SNSPD) to detect photons, constructs a SNSPD detection pulse position modulation (PPM) symbol detection model, and constructs a detection matrix of a PPM-SNSPD channel; S2, records an optical count vector of each time slot for each nanowire in the SNSPD detector; For one nanowire in the SNSPD detector, in one time slot, and the nanowire is not in the dead time when the time slot starts, p 00 , p 01 , p 10 , p 11 are defined as follows: p 00 : the probability that the nanowire does not detect a photon when the sending end does not send a pulse; p 01 : the probability that the nanowire does not detect a photon when the sending end sends a pulse; p 10 : The probability that the nanowire detects a photon when the sending end is not sending a pulse; p 11 : The probability that the nanowire detects a photon when the sending end sends a pulse; obtaining a probing matrix The calculation formula is: wherein, and respectively denote the average number of signal and noise photons arriving at the nanowire within one time slot, P Ber Bernoulli distribution of the counting probability of the photons; S3, analyzes a pulse position modulation (PPM) symbol detection state according to the optical count vector of the SNSPD detector; the symbol detection state includes five kinds, namely, an active state D0D, a dead time state DND, an active state D0E in which no photon is detected, a state DNE in which the whole symbol cycle is in the dead time state but the hth time slot is recovered to the active state, and a state Di in which the whole symbol cycle is in an un-detectable state; S4, for each nanowire, calculates a log-likelihood ratio (LLR) of a nanowire single channel using the optical count vector and each kind of the symbol detection state, and configures a calculation formula of the log-likelihood ratio (LLR) of the nanowire single channel for each kind of the symbol detection state respectively; S5, adds the log-likelihood ratio of each nanowire single channel to obtain a log-likelihood ratio of the whole SNSPD detector.

2. The log-likelihood ratio calculation method of the PPM-SNSPD communication system according to claim 1, characterized in that, According to the Poisson distribution, the probability that a single time slot contains no dead time, the number of photons arriving at the detector in a time interval of duration T is given by due to the influence of the dead time, a relationship between a number of detected photons y in a single time slot and a number of photons n1 arriving in a single time slot is: ； Thus, in the state of consideration of dead time, the counting probability of y photons detected in follows a Bernoulli distribution: where P poi (0, μT s represents the probability that no photon arrives at the detector in a time slot, is the average number of photons arriving at the detector in a second, T s is the width of a time slot. 3.The method of claim 1, wherein, the S3 comprises: A light count vector for each time slot of each nanowire of the SNSPD detector , received The demodulation is performed to obtain a soft decision estimate, and the conditional probability of receiving when the transmitted symbol is is defined as A more accurate soft decision estimate is obtained by continuously tracking the symbol detection state transition of each nanowire , wherein y i is the photon count for the i-th time bin of the symbol, S is the symbol detection state. 4.The method of claim 1 or 3, wherein, the S4 comprises: For a single nanowire in an SNSPD detector, use representing that the nanowire detected a photon in the jth time slot of the symbol period, representing that the nanowire did not detect a photon in the symbol period, the method for calculating the single-channel log-likelihood ratio (LLR) of the nanowire under different symbol detection states is as follows: When the nanowire is in the active state D0D, the symbol sent by the transmitting end is Under the condition of the above equation, the single-channel LLR calculation formula for detecting a photon at time j is: where D0D represents that the nanowire is in an active state at the beginning of the current symbol period and a photon is detected thereafter, i represents a time slot in which a pulse is transmitted, p 00 represents a probability that the nanowire does not detect a photon when the transmitting end does not transmit a pulse; p 01 represents a probability that the nanowire does not detect a photon when the transmitting end transmits a pulse; p 10 represents a probability that the nanowire detects a photon when the transmitting end does not transmit a pulse; p 11 represents a probability that the nanowire detects a photon when the transmitting end transmits a pulse. 5.The method of claim 1 or 3, wherein, the S4 further comprises: When the nanowire is in the dead time state DND, the transmitted symbol is The single channel LLR calculation formula for detecting a photon at time j is: where DND represents that the nanowire is in dead time at the beginning of the symbol period, recovers the active state at the ith time slot, and then detects a photon, represents that the nanowire detects a photon at the jth time slot of the symbol period, and i represents the time slot of the transmitted pulse, p 00 represents the probability that the nanowire does not detect a photon when the transmitting end does not transmit a pulse; p 01 represents the probability that the nanowire does not detect a photon when the transmitting end transmits a pulse; p 10 represents the probability that the nanowire detects a photon when the transmitting end does not transmit a pulse; p 11 represents the probability that the nanowire detects a photon when the transmitting end transmits a pulse. 6.The method of claim 1 or 3, wherein, the S4 further comprises: When the nanowire is in state D0E, the transmitted symbol is The single-channel LLR calculation formula for detecting a photon at time j is: where D0E represents the nanowire is in the active state throughout the symbol period but no photon is detected, Dij represents the nanowire detects a photon in the jth time slot of the symbol period, i represents the time slot in which the pulse is transmitted, p 00 P0E represents the probability that the nanowire does not detect a photon when the transmitting end does not transmit a pulse; p 01 P1E represents the probability that the nanowire does not detect a photon when the transmitting end transmits a pulse; p 10 P0E represents the probability that the nanowire does not detect a photon when the transmitting end does not transmit a pulse; p 11 P1E represents the probability that the nanowire does not detect a photon when the transmitting end transmits a pulse; 7.The method of claim 1 or 3, wherein, the S4 further comprises: When the nanowire is in the DNE state, the transmitted symbol is and the single-channel LLR calculation formula for not receiving a photon is: where DNE represents that the nanowire is in dead time at the beginning of the whole symbol period and recovers the active state at the hth time slot, represents that the nanowire detects a photon at the jth time slot of the symbol period, represents that no photon is detected in the symbol period, and i represents the time slot of the transmitted pulse, p 00 represents the probability that the nanowire does not detect a photon when the transmitting end does not transmit a pulse; p 01 represents the probability that the nanowire does not detect a photon when the transmitting end transmits a pulse. 8.The method of claim 1 or 3, wherein, the S4 further comprises: When the nanowire is in the Di state, the symbol sent by the sending end is The single-channel LLR calculation formula under the condition that the nanowire is in the Di state and no photons are detected is: =0； where Di represents that the nanowire is in an undetectable state for the entire symbol period; i = 1,...N-1, N represents a dead time factor, represents that the nanowire detects a photon in the jth time slot of the symbol period, represents that no photon is detected in the symbol period. 9.The method of claim 1 or 3, wherein, the S4 further comprises: the log-likelihood ratio of the whole SNSPD detector in the S5 specifically comprises: wherein, represents the single-channel LLR of the i-th nanowire in the SNSPD detector, l represents the single-channel LLR of the i-th nanowire in the SNSPD detector, represents the photon detection result of the nanowire, represents the transmitted symbol, represents the symbol detection state of the nanowire, and the processes of different nanowire detections of photons remain independent of each other, and L is the total number of nanowires contained in the SNSPD detector.

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