An iterative detection method for quantum power domain non-orthogonal multiple access

Abstract

This invention belongs to the field of integrated wireless and quantum communication technology, specifically an iterative detection method for quantum power domain non-orthogonal multiple access systems. The invention involves constructing a quantum power domain non-orthogonal multiple access system, including a transmitter, a free-space channel, and a receiver. The transmitter sequentially performs channel coding, random interleaving, and quantum coherent state modulation. The receiver includes a Bondurant quantum receiver and a multi-user iterative detector based on the Turbo principle. This invention particularly establishes a photon statistical model at the receiver that considers dead-time effects, incorporating the non-ideal characteristics of the detector into the multi-user detection process. Combined with serial interference cancellation and soft information interaction between the detector and decoder, it achieves iterative detection and decoding of multi-user superimposed signals. This method improves the separation capability, detection accuracy, and decoding reliability of multi-user signals in quantum power domain non-orthogonal multiple access systems.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and quantum communication integration technology, specifically relating to an iterative detection method for non-orthogonal multiple access systems in the quantum power domain. Background Technology

[0002] As applications such as smart factories and the Industrial Internet of Things (IIoT) place increasingly higher demands on the security, connection density, and transmission reliability of communication systems, traditional classical communication technologies are gradually facing limitations in terms of multi-user access capabilities, anti-interference performance, and high-security transmission. Quantum communication, utilizing the principles of quantum mechanics for information transmission, possesses inherently high security and strong anti-eavesdropping capabilities, thus demonstrating significant application prospects in the construction of highly reliable communication networks. In particular, quantum communication schemes based on coherent state modulation have attracted widespread attention in recent years due to their good compatibility with existing optical communication devices, relatively low implementation difficulty, and significant engineering application potential.

[0003] In multi-user access, non-orthogonal multiple access (NOAMI) technology enables multiple users to share the same time-frequency resources by superimposing and transmitting multiple user signals in the power domain, thereby effectively improving system capacity and spectrum utilization. Existing classical NOAMI systems typically employ methods such as serial interference cancellation to separate and detect multi-user signals at the receiver, and improve user distinguishability through reasonable power allocation. However, directly applying these methods to quantum communication scenarios presents significantly different challenges compared to classical communication. On one hand, quantum coherent signals typically operate in weak light, even approaching the single-photon level, requiring photon counting detectors for signal detection at the receiver. On the other hand, the quantum reception process is affected by background noise, channel fading, and the non-ideal characteristics of the detector, making the detection of superimposed multi-user signals more complex.

[0004] In particular, during actual photon detection, detectors typically suffer from a dead-time effect. This means that after responding to one incident photon, the detector needs a recovery time during which it cannot effectively respond to subsequent incident photons. Due to this effect, the photon count observed at the receiver does not strictly satisfy an ideal linear relationship with the actual incident light field intensity, causing the actual photon statistical distribution to deviate from the ideal Poisson distribution. For quantum power-domain non-orthogonal multiple access systems, after multiple user signals are superimposed in the power domain, the receiver already needs to effectively distinguish the contributions of different user signals. The dead-time effect further weakens the statistical distinguishability between different users, increasing the difficulty of subsequent signal separation and decision-making.

[0005] Furthermore, most existing multi-user detection methods are based on linear Gaussian channel models or ideal receiver models, primarily designed for classical wireless communication systems. They are ill-suited to the multi-user detection requirements of quantum coherent state modulation, photon counting reception, and non-ideal detector conditions. Especially in the low photon number region, the statistical differences between superimposed signals from different users are small. If traditional hard-decision or single-detection methods are still used, multi-user interference residues can easily accumulate, leading to a decline in serial interference cancellation performance and a significant increase in the system's bit error rate. At the same time, traditional methods typically fail to fully utilize the soft information interaction mechanism between the decoder and detector, and fail to incorporate the detector dead-time effect into the multi-user detection model. Therefore, they struggle to achieve ideal detection performance in practical quantum multi-user access environments. Summary of the Invention

[0006] The purpose of this invention is to propose an iterative detection algorithm for non-orthogonal multiple access in the quantum power domain, which enables more accurate and reliable signal detection under the condition of superimposed transmission of multi-user signals, thereby improving the receiving performance and practical application capability of quantum multi-user communication systems.

[0007] The iterative detection algorithm for non-orthogonal multiple access in the quantum power domain proposed in this invention includes the design of a non-orthogonal multiple access communication system in the quantum power domain. The system structure includes a transmitter, a free-space channel, and a receiver. The transmitter includes a channel coding unit and an interleaver. A quantum M-QAM coherent state modulator is used. User signals undergo channel coding, random interleaving, and quantum coherent state modulation sequentially. The coherent state transmitted by the user reaches the receiver via a free-space channel. The receiver includes a Bondurant quantum receiver and a multi-user iterative detector based on the Turbo principle. It receives and decodes the information transmitted through the free-space channel, assuming the CSI is known. This invention specifically establishes a photon statistical model at the receiver considering dead-time effects, incorporating the non-ideal characteristics of the receiver detector into the multi-user detection process. Combined with serial interference cancellation and soft information interaction between the detector and decoder, it achieves iterative detection and decoding of multi-user superimposed signals. This enables effective separation and reliable detection of multi-user superimposed signals in a quantum power domain non-orthogonal multiple access system, thereby improving the system's multi-user reception performance and decoding accuracy. The specific steps are as follows:

[0008] (1) The specific process of channel coding, random interleaving, and quantum coherent state modulation at the transmitting end is as follows:

[0009] Let the first The information sequence for each user is: , Where K is the sequence length and K is the number of transmitting users; the coded sequence is generated by the channel coding unit: , yes The sequence length;

[0010] The system assigns a unique and unrelated interleaver to each user. ,use Indicates the first Interleaver for individual users. After interleaving, an interleaved sequence is obtained, and then... express.

[0011] The sequence was then subjected to quantum M-QAM coherent state modulation, so that... The modulated quantum coherent state is then represented as:

[0012]

[0013] in, Let be the amplitude of the coherent state, where This represents the total number of constellation points in M-QAM modulation, i.e., the number of different quantum coherent state symbols. `i` is the imaginary unit, used to represent the imaginary part (orthogonal component) of the M-QAM coherent state symbol in the complex plane. During M-QAM modulation, each... Each information bit is mapped to an M-QAM coherent state symbol, and there are M different coherent state symbols. Therefore, after coherent state modulation, each user's information sequence is transformed into... A symbol of an M-QAM quantum coherent state.

[0014] Taking 4-QAM (M=4) as an example, every 2 information bits are mapped to 4 different symbols, a set It can be written as:

[0015]

[0016] Then the first The set of 4-QAM coherent state signals corresponding to each user can be written as:

[0017]

[0018] Next, the The modulation signal of each user introduces a power allocation coefficient. The power-weighted multi-user signals are then superimposed and transmitted to the free-space channel.

[0019] (2) The receiving end uses a Bondurant quantum receiver and a multi-user iterative detector based on the Turbo principle to receive and decode the information transmitted in the free space channel, provided that the CSI is known; the specific process is as follows:

[0020] (a) Selecting a suitable quantum receiver for different quantum coherent state modulation schemes. Specifically, based on the MQAM quantum coherent state modulation scheme, a Bondurant receiver is selected, and the receiver structure of the multi-user communication system and the corresponding multi-user iterative detection algorithm are designed. The measurement and estimation of the free space channel is not the focus of this paper; therefore, the reception and decoding of multi-user signals will be carried out under the premise that the CSI is known.

[0021] After transmission through the free space channel, at the receiving end... The signal received at each time slot can be represented as:

[0022]

[0023] in Indicates the first Channel coefficients for each user This represents the transmit power coefficient allocated to this user. To simplify subsequent derivations, the equivalent channel coefficient is defined as follows:

[0024]

[0025] Therefore, the receiving end The signal received at each time slot can be written as:

[0026]

[0027] The BonDurant quantum receiver uses a beam splitter to separate the received signal from the local oscillator field. After interference, the signal after displacement can be expressed as:

[0028]

[0029] Detection of the first When the number of users is reached, the receiving end is the first... The total signal received at each time slot can be expressed as:

[0030]

[0031] in, The signal of the user currently being detected. This indicates that the estimated signal of the user has been detected. This indicates that residual user interference has not yet been detected. Indicates the receiver is at the 1st The first time slot for the first The estimated value of each detected user symbol is used for subsequent serial interference cancellation.

[0032] For the For each user, the local oscillation field in the BonDuraut quantum receiver is set as follows:

[0033]

[0034] Therefore, the signal after the local oscillator is:

[0035]

[0036] (b) Dead time effect processing, including establishing a photon statistical model of the dead time effect;

[0037] After interference is achieved through a beam splitter, the interference signal is analyzed by a photon detector. Photon counting is performed. Ideally, a photon detector can accurately distinguish and count every received photon, in which case the photon statistical distribution of the received signal follows a Poisson distribution. However, the performance of practical photon detectors is limited, and the photon counting result is affected by the dead time. After each photon incident, the photon detector experiences an avalanche, and for a fixed period of time afterward, it cannot respond to subsequent incoming photons; this period is called the dead time.

[0038] The dead-time shielding effect causes a change in the statistical distribution of photons in the received signal. Therefore, dead-time shielding is processed before multi-user iterative detection unit detection; specifically, in the case of non-ideal photon counting by the detector, the statistical distribution of the received signal changes from the ideal Poisson distribution to a binomial distribution.

[0039] The sequence of photon numbers output by a photon detector can be expressed as: Use them separately and This represents the average number of photons between the received signal and background noise. The quantum efficiency of a photon detector is expressed in the first... The result of detecting the number of photons in each time slot is The probability is:

[0040]

[0041]

[0042] in, Indicates in Select from the elements The number of combinations of is calculated as follows:

[0043]

[0044] when hour, The probability follows a binomial distribution of infinitely repeated trials. From the relationship between the binomial and Poisson distributions, we can derive... hour, Satisfying the mean is The signal follows a Poisson distribution, which is precisely the probability distribution model for the received signal under ideal photon counting. This proves that when the dead time is sufficiently small, much smaller than the signal pulse width, the impact of the dead time on signal reception is negligible.

[0045] (c) The detection results from the photon detector are input into the multi-user detection unit for further detection. This detection unit employs a multi-user iterative detection structure based on the Turbo principle. The multi-user detector (MUD) and the decoder (DEC) interact through soft information in the form of log-likelihood ratio.

[0046] In a multi-user iterative detection structure based on the Turbo principle, let... Let the prior information of a given bit to be detected be defined in the logarithmic field as:

[0047]

[0048] This prior information, provided by the output of the previous decoder, characterizes the reliability of the decision for the current bit under the coding constraints. As the iteration progresses, if the decoder's decision on a certain bit tends to stabilize, the corresponding prior LLR magnitude will gradually increase.

[0049] The multi-user detection unit detects the received signal. And the extrinsic information of this bit calculated from the current prior information is:

[0050]

[0051] This extrinsic information only reflects incremental information from channel observations and does not include prior probabilities, thus avoiding information reuse. The output extrinsic information is deinterleaved and used as the prior input to the decoder.

[0052]

[0053] The decoder performs a soft decision on this bit under the constraints of the encoding, and its posterior log-likelihood ratio is defined as:

[0054]

[0055] According to Bayes' theorem:

[0056]

[0057] We can obtain:

[0058]

[0059] Right now:

[0060]

[0061] It is evident that, in the logarithmic field, the posterior information equals the sum of the extrinsic information and the prior information. Therefore, the extrinsic information output by the decoder is:

[0062]

[0063] This external information, after being interleaved, is fed back to the multi-user detector as prior input for the next iteration:

[0064]

[0065] This completes the closed-loop structure.

[0066] Next, taking 4-QAM quantum coherent state modulation as an example, we present the internal and external iterative detection algorithm for serial interference cancellation at the receiver. In the 4-QAM quantum coherent state modulation process, every two bits are modulated into a QAM symbol. The two bits corresponding to each symbol are represented as follows: and

[0067] for Its MUD output information is as follows:

[0068]

[0069] Two information bits and They are mutually independent and include:

[0070]

[0071] Therefore, the output external information can be simplified to

[0072]

[0073] for The definition of its prior information is:

[0074]

[0075] Further, it can be Written as:

[0076]

[0077] when , At that time, in the The average number of photons received in each time slot for:

[0078]

[0079] in, This indicates that residual multi-user interference generated by users has not yet been detected. In the iterative detection process of serial interference cancellation, the detection of the current user depends not only on the received signal itself but also on the prior information fed back by the decoder. Since QAM modulation can be decomposed into I / Q two-path BPSK mapping, the following construction of prior information and soft interference estimation process are illustrated using BPSK as an example. The related derivation methods can be naturally extended to the general M-QAM case.

[0080] Let the first The user in the first The modulation symbols for each time slot are mapped using BPSK, i.e. Its prior LLR is defined as:

[0081]

[0082] To perform soft interference cancellation in multi-user detection, it is necessary to construct soft estimates, i.e., statistical expectations, of the symbols of users not yet detected based on this prior information. The expectation can be written as:

[0083]

[0084] Based on the relationship between LLR and sign probability, we have:

[0085]

[0086]

[0087] Substituting, we get:

[0088]

[0089] Rearranging it into hyperbolic function form, we get:

[0090]

[0091] Therefore, the symbols of users who have not yet been detected can be modeled using soft statistics as follows:

[0092]

[0093] when When there is no prior information, the expected value is 0; as... As it increases, the expected value gradually approaches... This indicates that the reliability of symbolic decision-making has improved.

[0094] when , At that time, the average number of photons for:

[0095]

[0096] Similarly, we can obtain the results when... , , , and , hour Value:

[0097]

[0098]

[0099]

[0100] At this point, the average number of photons... Calculation complete. Substituting the photon statistical distribution into the formula for calculating external information yields the external information. Value:

[0101]

[0102] in,

[0103] Similarly, the same method can be used to further obtain... The corresponding external information expression (class begins with equation (40)).

[0104] For 4-QAM modulation, based on the two bits of extrinsic information and the corresponding prior information, the posterior probability of each candidate symbol can be further calculated, thus obtaining a soft estimate of the current user's symbol. This soft estimate result will be immediately fed back into the interference cancellation process of subsequent users after the current round of detection to update the remaining multi-user interference terms.

[0105] The main technical features and performance advantages of this invention are as follows:

[0106] (1) This invention combines the Bondurant quantum receiver with a multi-user iterative detection structure based on the Turbo principle, which can effectively utilize the soft information in the received signal in the non-orthogonal multiple access scenario in the quantum power domain. By interacting with the external information and prior information in multiple rounds, the detection accuracy of the multi-user signal is improved, thereby enhancing the system's ability to suppress multi-user interference and improving the decoding reliability of the receiver.

[0107] (2) In the detection process, the present invention takes into account the influence of the dead time effect of the photon detector on the statistical distribution of photon count, and incorporates the actual non-ideal detection conditions into the multi-user detection model, so that the proposed detection method is not only applicable to the ideal Poisson photon counting scenario, but also can more realistically reflect the actual quantum reception process, thus having stronger engineering applicability and practical application value.

[0108] (3) The present invention adopts a detection method that combines serial interference cancellation and internal and external iteration. In the current user detection process, it can make full use of the estimation results of the detected users to gradually cancel the interference, and use the soft estimation information of the undetected users to characterize the residual interference. This helps to reduce the impact of crosstalk between multiple users on the decision result, improve the overall detection performance of the system, and improve the multi-user reception effect in the quantum power domain non-orthogonal multiple access system.

[0109] This invention is applicable to multi-user quantum coherent state communication scenarios, and is especially applicable to communication systems with multi-user power superposition transmission and photon counting detection. Attached Figure Description

[0110] Figure 1 This is a model diagram of the transmitter of a non-orthogonal multiple access system in the quantum power domain.

[0111] Figure 2 This is a model diagram of the receiver end of a nonorthogonal multiple access system in the quantum power domain.

[0112] Figure 3 This is a model diagram of the Bondurant receiver.

[0113] Figure 4 This is a comparison chart of the bit error rate performance of the present invention. Detailed Implementation

[0114] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0115] The quantum power domain nonorthogonal multiple access communication system of the present invention includes a transmitter and a receiver. At the transmitter, user signals are sequentially subjected to channel coding, random interleaving, and quantum coherent state modulation. The receiver includes quantum reception and multi-user iterative detection.

[0116] In this embodiment of the invention, four users participate in the communication, each sending 1000 frames of information, with each frame containing 1024 bits. The user signals are modulated using 4-QAM quantum coherent state modulation. The average photon number of the background noise is... Set to 50, defining the average bit energy of user information as... The unit is dBJ. Atmospheric turbulence is modeled using a Gamma-Gamma channel, with weak turbulence parameters set to [value missing]. , The communication wavelength is set to 1550nm.

[0117] Power allocation factor The water-filling algorithm commonly used in PD-NOMA systems can be given, and its bit error rate performance in iterative detection algorithms can be compared with the performance of non-iterative detection PD-NOMA systems and average power distribution systems.

[0118] See Figure 4 As can be seen, the bit error rate of the PD-NOMA system under the iterative detection algorithm is significantly lower than that of the non-iterative detection PD-NOMA system and the average power distribution system, demonstrating better detection performance.

[0119] This invention focuses on the receiver design of quantum PD-NOMA systems. Considering the system's receiver structure, signal statistical characteristics, and the features of multi-user non-orthogonal superposition transmission, a serial interference cancellation iterative multi-user detection algorithm is proposed. Specifically, at the receiver, serial interference cancellation gradually weakens the impact of strong interfering users on the detection of the target user. Simultaneously, incorporating the Turbo iteration concept, the decision results for each user are continuously updated through soft information interaction between the detector and decoder, thereby improving the detection capability of multi-user superimposed signals.

Claims

1. An iterative detection method for non-orthogonal multiple access in the quantum power domain, characterized in that, This includes the design of a quantum power domain nonorthogonal multiple access communication system, the system architecture of which includes a transmitter, a free-space channel, and a receiver; wherein: The transmitting end includes a channel coding unit and an interleaver. A quantum M-QAM coherent state modulator, in which the user signal is sequentially channel-coded, randomly interleaved and quantum coherent state modulated, and the coherent state transmitted by the user reaches the receiver through a free space channel; The receiver includes a Bondurant quantum receiver and a multi-user iterative detector based on the Turbo principle. It receives and decodes multi-user signals transmitted in the free space channel, provided that the CSI is known. Specifically, a photon statistical model considering the dead-time effect is established to incorporate the non-ideal characteristics of the receiver detector into the multi-user detection process. Combined with serial interference cancellation and soft information interaction between the detector and decoder, iterative detection and decoding of multi-user superimposed signals are achieved.

2. The iterative detection method according to claim 1, characterized in that, The transmitting end performs channel coding, interleaving, and quantum M-QAM coherent state modulation of user information; the specific process is as follows: Let the first The information sequence for each user is: , Where K is the sequence length and K is the number of transmitting users; the coded sequence is generated by the channel coding unit: , yes The sequence length; Each user is assigned a unique and unrelated interleaver. ,use Indicates the first Interleaver for individual users; After interleaving, an interleaved sequence is obtained, and then... express; The sequence was then subjected to quantum M-QAM coherent state modulation, so that... The modulated quantum coherent state is then represented as: in, Let M be the amplitude of the coherent state, M be the number of different coherent state symbols, and i be the imaginary unit used to represent the imaginary part of the M-QAM coherent state symbol in the complex plane; during M-QAM modulation, each Each information bit is mapped to an M-QAM coherent state symbol; after coherent state modulation, each user's information sequence is transformed into... One M-QAM quantum coherent state symbol; Next, the The modulation signal of each user introduces a power allocation coefficient. The power-weighted multi-user signals are then superimposed and transmitted to the free-space channel.

3. The iterative detection method according to claim 2, characterized in that, The receiving end receives and decodes multi-user signals under the premise that the CSI is known. The specific process is as follows: (a) After transmission via a free-space channel, at the receiving end... The signal received at each time slot is represented as follows: in Indicates the first Channel coefficients for each user This represents the transmit power coefficient allocated to this user. To simplify subsequent derivations, the equivalent channel coefficient is defined as follows: Therefore, the receiving end The signals received at each time slot are written as follows: The BonDurant quantum receiver uses a beam splitter to separate the received signal from the local oscillator field. After interference, the signal after displacement is represented as: Detection of the first When the number of users is reached, the receiving end is the first... The total signal received at each time slot is represented as: in, The signal of the user currently being detected. This indicates that the estimated signal of the user has been detected. This indicates that residual user interference has not yet been detected. Indicates the receiver is at the 1st The first time slot for the first The estimated values ​​of the detected user symbols are used for subsequent serial interference cancellation; For the For each user, the local oscillation field in the BonDuraut quantum receiver is set as follows: Therefore, the signal after the local oscillator is: (b) Establish a photon statistical model for the dead time effect, that is, perform dead time shielding effect processing before entering the multi-user iterative detector; specifically, in the case of non-ideal photon counting in the detector, the statistical distribution of the received signal is transformed from the Poisson distribution in the ideal case to a binomial distribution. Let the sequence of photon outputs from the photon detector be expressed as: ; respectively and This represents the average number of photons between the received signal and background noise. The quantum efficiency of a photon detector is expressed in the first... The result of detecting the number of photons in each time slot is The probability is: in, Indicates in Select from the elements The number of combinations of is calculated as follows: when hour, The probability follows a binomial distribution for infinitely repeated trials; from the relationship between the binomial distribution and the Poisson distribution, we know that when hour, Satisfying the mean is The Poisson distribution is the probability distribution model of the received signal under ideal photon counting conditions. It shows that when the dead time is much smaller than the signal pulse width, the effect of the dead time on signal reception is negligible. (c) The detection results of the photon detector are input into the multi-user iterative detector for detection; the multi-user iterative detector (MUD) and the decoder (DEC) interact through soft information in the form of log-likelihood ratio; In a multi-user iterative detector, let... For a given bit to be detected, the prior information in the logarithmic field is defined as: This prior information is provided by the output of the previous decoder and represents the reliability of the decision of the current bit under the coding constraints. As the iteration progresses, if the decoder's judgment on a certain bit tends to be stable, the corresponding prior LLR magnitude will gradually increase. Multi-user iterative detectors based on received signals And the extrinsic information of this bit calculated from the current prior information is: This external information only reflects the incremental information obtained from channel observations and does not include prior probabilities, thus avoiding the reuse of information; the output external information is deinterleaved and used as the prior input of the decoder: The decoder performs a soft decision on this bit under the constraints of the encoding, and its posterior log-likelihood ratio is defined as: According to Bayes' theorem: have to: Right now: It is evident that, in the logarithmic field, the posterior information equals the sum of the extrinsic information and the prior information; therefore, the extrinsic information output by the decoder is: This external information, after being interleaved, is fed back to the multi-user iterative detector as prior input for the next iteration: This completes the closed-loop structure.

4. The iterative detection method according to claim 3, characterized in that, For the 4-QAM quantum coherent state modulation method, the specific process of the internal and external iterative detection algorithm for serial interference cancellation at the receiver is as follows: In the 4-QAM quantum coherent state modulation process, every two bits are modulated into a QAM symbol; the two bits corresponding to each symbol are represented as follows: and ; for Its MUD output information is as follows: Two information bits and They are mutually independent and include: Therefore, the output of external information can be simplified as follows: for The definition of its prior information is: Further Written as: when , At that time, in the The average number of photons received in each time slot for: in, This indicates that residual multi-user interference generated by users has not yet been detected; In the iterative detection process of serial interference cancellation, the detection of the current user depends not only on the received signal itself, but also on the prior information fed back by the decoder. Since QAM modulation can be decomposed into I / Q two-way BPSK mapping, the construction of prior information and the soft interference estimation process for the BPSK mapping is as follows: Let the first The user in the first The modulation symbols for each time slot are mapped using BPSK, i.e. Its prior LLR is defined as: To perform soft interference cancellation in multi-user detection, it is necessary to construct a soft estimate of the symbols of users who have not yet been detected, i.e., their statistical expectation, based on this prior information. This expectation is: Based on the relationship between LLR and sign probability, we have: Substituting into equation (30), we get: Rearranging it into hyperbolic function form, we get: Therefore, the symbols of users who have not yet been detected can be modeled using soft statistics as follows: when When there is no prior information, the expected value is 0; as... As it increases, the expected value gradually approaches... This indicates that the reliability of symbolic decision-making has improved; when , At that time, the average number of photons for: Similarly, we obtain the following respectively: , , , and , hour Value: At this point, the average number of photons... Calculation complete; substituting the photon statistical distribution into the formula for calculating external information yields the external information. Value: in, Similarly, the same method can be used to further obtain... The corresponding class begins with the external information expression in equation (40); For 4QAM modulation, based on the two bits of extrinsic information and the corresponding prior information, the posterior probability of each candidate symbol can be further calculated, thereby obtaining the soft estimate of the current user's symbol. This soft estimate will be fed back to the interference cancellation process of subsequent users immediately after the current round of detection, and used to update the remaining multi-user interference terms.

Images