A method for power allocation of a bottom-layer cognitive user based on a cell-free massive MIMO system

Abstract

This invention discloses a low-level cognitive user power allocation method based on a cell-free massive MIMO system, comprising: PU k and SU respectively to AP l and AP m Send pilot signals, which are transmitted to the AP via the channel; the AP l and AP m The received signal is projected onto the input and output planes for minimum mean square error estimation; AP l and AP m Perform conjugate precoding on the transmitted signal; obtain the PU based on the structure of the received signal. k The invention establishes the receiving rate expression for the SU, establishes the relationship between the power allocation function and the environment-related function, and calculates the minimum number of AP connections M required by the SU through the relationship; calculates the optimal power allocation scheme for the SU; after obtaining the minimum number of AP connections M required by the SU, it calculates how much power should be allocated to the SU for each AP in the set. This invention divides users into primary users and secondary users, which can reduce the resources occupied by secondary users and reduce interference to primary users, effectively improving the receiving rate of secondary users.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology and relates to a method for underlying cognitive user power allocation based on a cellless massive MIMO system. Background Technology

[0002] With the surge in the number of communication users over the years, inter-cell interference has become increasingly severe for cell-edge users in traditional cellular systems due to the influence of multiple base stations. To address this issue, cell-free massive MIMO systems have emerged. In cell-free massive MIMO, a large number of access points (APs) are distributed within an area, and users are randomly distributed within this area, but their number is far less than the number of access points. The APs exchange channel statistics and power control coefficients with the central processing unit (CPU) through the backhaul network. Cell-free massive MIMO and cognitive radio technology are key technologies in next-generation mobile communications, and their combination is one of the hot topics in communication research. Cell-free massive MIMO has numerous antennas, high coverage, and close proximity between users and APs, resulting in strong resistance to shadow fading. However, spectrum utilization has not been significantly improved. Cognitive radio, on the other hand, can fully utilize the spectrum by distinguishing between primary and secondary users, improving spectrum utilization while accommodating more users.

[0003] Currently, in cellless massive MIMO systems, most considerations focus on power allocation or AP selection to improve channel rates for unclassified users, without considering classifying users into primary and secondary users before power allocation and AP selection.

[0004] Chinese patent application CN113365334A discloses a pilot allocation and power control method in a cell-free massive MIMO system. This method uses zero-forcing precoding to process the transmitted signal in advance and optimizes the downlink rate during transmission using a max-min power control algorithm. Chinese patent CN110166088A discloses a user-centric power control algorithm for a cell-free massive MIMO system. This method maximizes the minimum user rate by searching for the optimal power control coefficient. The paper "Cell-Free Massive MIMO with Underlay Spectrum-Sharing" (Diluka Loku Galappaththige and Gayan Amarasuriya) presented at the international conference ICC 2019-2019 IEEE International Conference on Communications (ICC) combines a cell-free massive MIMO system with a cognitive wireless system and studies the feasibility of time-division duplex-based cell-free massive MIMO and underlying spectrum sharing. However, the above technologies have the following drawbacks: 1. They do not clearly distinguish between primary and secondary users, resulting in low spectrum utilization; 2. Both users and APs use single antennas, without considering the case of multiple antennas; 3. Dividing APs into primary APs and secondary APs leads to a waste of AP resources when there are too many primary users and too few secondary users. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a low-level cognitive user power allocation method based on a cellless massive MIMO system. After dividing users into primary and secondary users, the method aims to minimize the use of primary user resources and reduce interference with primary users. By comprehensively considering the channel's large-scale fading coefficient and AP power weighting coefficient, the optimal power allocation scheme is obtained by selecting the minimum number of APs, maximizing the secondary user's receiving rate and improving secondary user communication quality. This effectively solves the problems of insufficient spectrum utilization and distributed transmission of multi-antenna APs.

[0006] To achieve the above objectives, the present invention adopts the following technical solution.

[0007] A method for low-level cognitive user power allocation based on a cellless massive MIMO system is proposed. Within the cellless massive MIMO system area, L access points (APs) with N antennas are randomly distributed, along with K primary users (PUs) and one secondary user (SU). Both the primary and secondary users are single-antenna users, and L >> K; where L > 0, N > 0, and K > 0. and Let AP and PU be the sets respectively, and AP be the set of PU. l Let PU represent the l-th AP in the set.k This represents the Kth PU in the set; SU, as a single-antenna user that briefly appears in the area, selects the minimum number of APs to connect to after entering the area, using a dynamic set. This represents the selected set of APs, where a certain element is represented by an AP. m To indicate;

[0008] The method includes the following steps:

[0009] Step 1, PU k and SU respectively to AP l and AP m A pilot signal is sent, and the pilot signal reaches the AP after being transmitted through the channel;

[0010] Step 2: First, set up the AP l and AP m The received signal is projected onto and Then, perform minimum mean square error estimation.

[0011] Step 3, AP l and AP m Perform conjugate precoding on the transmitted signal;

[0012] Step 4: First, obtain the PU based on the structure of the received signal. k The receiving rate expression of the SU is obtained, and then the relationship between the power allocation function and the environment-related function is established. After that, the minimum number of AP connections M required by the SU is calculated through the relationship.

[0013] Step 5: Calculate the optimal power allocation scheme for the SU;

[0014] After obtaining the minimum number of AP connections M required by SU, it is necessary to set The calculation involves determining how much power each AP should be allocated to the SU.

[0015] Specifically, in step one, the PU k and SU respectively to AP l and AP m Sending pilot signals, which then travel through the channel to reach the AP, involves the following process:

[0016] S1.1.PU k and SU respectively to AP l and AP m Send pilot signal:

[0017] Using time-division multiplexing, each coherent interval is divided into three parts: uplink training, uplink data transmission, and downlink data transmission, without considering uplink data transmission; let τ c=196 is the coherence interval length, τ u τ is the uplink training coherence interval length. d =τ c -τ u τ is the length of the downlink data transmission coherence interval. c <τ d ;PU k and SU respectively to AP l and AP m Send length is τ u pilot sequence in

[0018] S1.2. The pilot signal reaches the AP after being transmitted through the channel:

[0019] The channel model is as follows:

[0020]

[0021] In the formula, g ab This represents the channel vector between the a-th AP and the b-th user. d represents the large-scale fading coefficient between the a-th AP and the b-th user. ab Let represent the distance between the a-th AP and the b-th user, and η represent the path fading factor, taking τ = 0.5. ab Let h represent the small-scale fading vector between the a-th AP and the b-th user, which is an N×1 vector, and assume h ab Subject to Rayleigh decay, where each element follows the law of conformity. random variables, This represents a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1.

[0022] AP l and AP m The signals received by the terminal are as follows:

[0023]

[0024]

[0025] In equations (2) and (3), p p W is the normalized transmit signal-to-noise ratio for each pilot symbol. pl W pm For the corresponding received signal N×τ u The noise matrix, where each element follows a set order. random variable; g lk g mSU They represent AP respectively l To PUk Channels and APs m The channel to SU; They represent PU k The conjugate transpose of the pilot sequence transmitted by SU.

[0026] Specifically, in step two, the AP is first... l and AP m The received signal is projected onto and Then, the minimum mean square error estimation is performed, which includes the following steps:

[0027] S2.1. Y pl and Y pm Projected to and superior:

[0028] Projection results They are respectively represented as

[0029]

[0030]

[0031] S2.2. Perform minimum mean square error estimation:

[0032] For channel g lk and g mSU The minimum mean square error (MMSE) estimation is performed, and the estimated value is calculated. and They are respectively:

[0033]

[0034]

[0035] In equations (6) and (7), This represents the expectation operation. and There are N independent and identical Gaussian components; the mean square sum of the nth component can be obtained from υ. lk and υ mSU express:

[0036]

[0037]

[0038] Specifically, in step three, the AP l and AP m The process of performing conjugate precoding on the transmitted signal includes:

[0039] APl To PU k The transmitted signals and AP m The signals sent to SU are respectively

[0040]

[0041]

[0042] In equations (10)(11), p lk Indicates AP l Assigned to PU k Power weight, p m Indicates AP m The power weight assigned to SU, where P represents the maximum normalized transmit power of AP. for The conjugate of channel estimation, s k s SU Indicates AP l AP m Send to PU k The symbol for SU

[0043] Specifically, the process of step four includes:

[0044] S4.1. Obtain PU based on the structure of the received signal. k The expression for the receiving rate of SU:

[0045] AP k The received signal and the signal received by SU are respectively

[0046]

[0047]

[0048] In equations (12) and (13), ω represents the transpose of the corresponding channel. k ω SU To correspond to additive noise in the received signal, where each element follows a set order. random variables;

[0049] Equations (12) and (13) can be expanded according to the structure of the signal as follows:

[0050]

[0051]

[0052] PU k The receiving rate at the SU end can be given by the following formula:

[0053]

[0054] (16) In the formula, SINR is the signal-to-interference-plus-noise ratio, and PU is the signal-to-interference-plus-noise ratio. k The signal-to-interference-plus-noise ratios at the SU end are as follows:

[0055]

[0056]

[0057] In equations (17) and (18), T1, T2, T3, and T4 correspond to PU in equation (14). k Desired signal, channel estimation error, multi-user interference and SU interference, T1 SU T2 SU T3 SU These correspond to the SU desired signal, channel estimation error, and PU interference in equation (15), respectively.

[0058] S4.2. Establish the relationship between the power allocation function and the environment-related function:

[0059] Since SU accesses the network as a secondary user, for PU k The interference caused must be less than a certain threshold, i.e., PU k The receiving rate needs to meet R k ≥R0, where R0 is a predefined PU k The receiving rate threshold is then substituted into R (16). k ≥R0 and calculated using channel statistics as the true channel value, we can obtain:

[0060]

[0061] Merge and categorize some variables in equation (19), and rewrite it as follows: with PU k Related environment-related functions and p m The relevant power allocation function f(G,p) m The relational expression:

[0062]

[0063] In equation (20), and f(G,p) m They are respectively:

[0064]

[0065] S4.3. Calculate the minimum number of AP connections M required by SU.

[0066] Specifically, the calculation process for the minimum number of AP connections M includes:

[0067] S4.3.1. Set AP The remaining power weight corresponding to each AP is multiplied by its large-scale fading coefficient, and then the results are sorted from largest to smallest to form an original set.

[0068]

[0069] S4.3.2. According to The order of APs in the original AP set The APs in the set are rearranged to obtain the AP set.

[0070] S4.3.3. From a set The first M APs are selected in order to form a set. M starts from 1;

[0071] S4.3.4. Set Substituting the relevant parameters of AP into equation (22), we get:

[0072]

[0073] S4.3.5. Determine whether equation (24) satisfies equation (20). If equation (20) is satisfied, then M+1 and return to S4.3.3; if equation (20) is not satisfied, then the obtained value of M is the minimum number of AP connections required by SU, and output M.

[0074] Specifically, in step five, the calculation process of the optimal power allocation scheme for SU includes:

[0075] S5.1. For the M-1 APs preceding the Mth AP, allocate all remaining power of each AP to SU;

[0076] S5.2. For the Mth AP, the steps for optimal power allocation using a convex optimization method based on bisection are as follows:

[0077] S5.2.1. Using f(G,p) m ) M To represent the result of equation (24) when M is taken, the following initial conditions are set, and the calculation starts from n=1:

[0078]

[0079] s0=f(G,p m ) M (26)

[0080] S5.2.2. Determine whether the calculation should continue. Introduce a predefined tolerance ε, ε = 0.01, and then compare ε with... The comparison is based on the following conditions:

[0081]

[0082] If equation (27) is satisfied, it means that the calculation result has reached the optimal power allocation, and jump to S5.2.4; if equation (27) is not satisfied, the optimal power allocation has not yet been reached, and continue to S5.2.3.

[0083] S5.2.3. To reduce the gap between the calculated result and the optimal power allocation at this time, s n Compare with equation (21) as follows:

[0084]

[0085] If equation (28) is satisfied, it means that the calculated result is less than the optimal power allocation, and additional calculations are needed. Let n = n + 1 and Jump to S5.2.2; if equation (28) is not satisfied, it means that the calculated result is greater than the optimal power allocation, and a reduction calculation is needed. Let n = n + 1 and Jump to S5.2.2;

[0086] S5.2.4. Obtain the optimal power allocation calculation result for the Mth AP (p m ) M Calculation method:

[0087]

[0088] S5.3. After the above steps, the final optimal power allocation scheme for SU can be obtained.

[0089]

[0090] Preferably, the cell-free massive MIMO system has a set area of ​​800×800m. 2 In a square area, there are 128 randomly distributed access points (APs) (L), 10 antennas (N), 12 primary users (K), and 1 secondary user (1).

[0091] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0092] 1. This invention divides users into primary users and secondary users, and no longer sets up auxiliary APs to serve secondary users. Instead, primary and secondary users share all APs within the range. Secondary users can access the system while the primary user's communication network remains stable. This increases the user capacity of the entire system and improves the spectrum utilization of the system.

[0093] 2. This invention utilizes the primary user's communication environment data to establish a power allocation function and an environment-related function, and designs a process in S4.3 to obtain the minimum number of AP connections M, thereby allowing secondary users to connect to the fewest APs and saving AP resources.

[0094] 3. In step five, this invention calculates the optimal power for each AP connected to the secondary user, and uses a convex optimization method based on bisection at the Mth AP to calculate the optimal power. This successfully reduces the impact of the secondary user on the primary user's receiving rate, achieves optimal power allocation for the secondary user, and improves the secondary user's receiving rate while saving AP resources as much as possible. Attached Figure Description

[0095] Figure 1 This is a system model diagram of one embodiment of the present invention.

[0096] Figure 2 This is a flowchart of a method according to an embodiment of the present invention;

[0097] Figure 3 This is a flowchart illustrating the calculation of the minimum AP connection number M in one embodiment of the method of the present invention.

[0098] Figure 4 This is a flowchart illustrating the calculation of the optimal power allocation scheme in one embodiment of the method of the present invention. Detailed Implementation

[0099] This invention provides a low-level cognitive user power allocation method based on a cellless massive MIMO system. It is applicable to situations where secondary users access the cellless network via low-level spectrum sharing. By comprehensively considering the channel's large-scale fading coefficient and AP power allocation weights, a novel low-level cognitive user power allocation method is proposed to maximize the channel rate of cognitive users. By dividing users into primary and secondary users, the method minimizes the resource consumption of primary users and reduces interference to primary users, thereby improving the channel rate of secondary users.

[0100] The present invention will now be described in further detail with reference to the accompanying drawings.

[0101] like Figure 1The diagram shows a system model of a low-level cognitive user power allocation method based on a cellless massive MIMO system according to the present invention. Within the cellless massive MIMO system area, L (L>0) APs with N (N>0) antennas are randomly distributed, along with K (K>0) primary users (PUs) and one secondary user (SU), where both the primary and secondary users are single-antenna users, and L >> K. and Let AP and PU be the sets respectively, and AP be the set of PU. l Let PU represent the l-th AP in the set. k Let represent the Kth PU in the set. The SU, as a single-antenna user briefly appearing in the area, should select the fewest possible APs to connect to upon entering the area, using a dynamic set. This represents the selected set of APs, where a certain element is represented by an AP. m To express.

[0102] In this invention example, the area of ​​the cellless massive MIMO system is set to 800×800m. 2 In a square area, there are 128 randomly distributed access points (APs) (L), 10 antennas (N), 12 primary users (K), and 1 secondary user (1).

[0103] like Figure 2 The diagram illustrates a method for allocating power to underlying cognitive users in a cell-free massive MIMO system, comprising the following steps:

[0104] Step 1: PU k and SU respectively to AP l and AP m A pilot signal is sent, and the pilot signal reaches the AP after being transmitted through the channel.

[0105] S1.1: PU k and SU respectively to AP l and AP m Send pilot signal.

[0106] Using time-division multiplexing, each coherent interval is divided into three parts: uplink training, uplink data transmission, and downlink data transmission, without considering uplink data transmission. Let τ c =196 is the coherence interval length, τ u τ is the uplink training coherence interval length. d =τ c -τ u τ is the length of the downlink data transmission coherence interval. c <τ d PU k and SU respectively to AP l and APm Send length is τ u pilot sequence in

[0107] S1.2: The pilot signal arrives at the AP after being transmitted through the channel.

[0108] The channel model is as follows:

[0109]

[0110] (1) In the formula, g ab This represents the channel vector between the a-th AP and the b-th user. d represents the large-scale fading coefficient between the a-th AP and the b-th user. ab Let represent the distance between the a-th AP and the b-th user, and η represent the path fading factor, taken as η = 0.5. ab Let h represent the small-scale fading vector between the a-th AP and the b-th user, which is an N×1 vector, and assume h ab Subject to Rayleigh decay, where each element follows the law of conformity. random variables, This represents a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1.

[0111] AP l and AP m The signals received by the terminal are as follows:

[0112]

[0113]

[0114] In equations (2) and (3), p p W is the normalized transmit signal-to-noise ratio for each pilot symbol. pl W pm For the corresponding received signal N×τ u The noise matrix, where each element follows a set order. The random variable. g lk g mSU They represent AP respectively l To PU k Channels and APs m The channel to SU. They represent PU k The conjugate transpose of the pilot sequence transmitted by SU.

[0115] Step 2: First, set up the AP l and AP m The received signal is projected onto and Then, perform minimum mean square error estimation.

[0116] S2.1: Y pl and Y pm Projected to and superior.

[0117] Projection results They are represented as follows:

[0118]

[0119]

[0120] S2.2: Perform minimum mean square error estimation.

[0121] For channel g lk and g mSU The minimum mean square error (MMSE) estimation is performed, and the estimated value is calculated. and They are respectively:

[0122]

[0123]

[0124] In equations (6) and (7), This represents the expectation operation. and There are N independent and identical Gaussian components. The mean square sum of the nth component can be obtained from υ. lk and υ mSU express:

[0125]

[0126]

[0127] Step 3: AP l and AP m The transmitted signal is subjected to conjugate precoding.

[0128] AP l To PU k The transmitted signals and AP m The signals sent to SU are as follows:

[0129]

[0130]

[0131] In equations (10)(11), p lk Indicates APl Assigned to PU k Power weight, p m Indicates AP m The power weight assigned to SU, where P represents the maximum normalized transmit power of AP. for The conjugate of channel estimation, s k s SU Indicates AP l AP m Send to PU k The symbol for SU

[0132] Step 4: First, obtain the PU based on the structure of the received signal. k The receiving rate expression of the SU is obtained, and then the relationship between the power allocation function and the environment-related function is established. After that, the minimum number of AP connections M required by the SU is calculated through the relationship.

[0133] S4.1: Obtain PU based on the structure of the received signal. k The expression for the receiving rate of SU.

[0134] AP k The received signals and the signals received by the SU are as follows:

[0135]

[0136]

[0137] In equations (12) and (13), ω represents the transpose of the corresponding channel. k ω SU To correspond to additive noise in the received signal, where each element follows a set order. A random variable.

[0138] Equations (12) and (13) can be expanded based on the signal composition as follows:

[0139]

[0140]

[0141] PU k The receiving rate at the SU end can be given by the following formula:

[0142]

[0143] (16) In the formula, SINR is the signal-to-interference-plus-noise ratio, and PU is the signal-to-interference-plus-noise ratio. k The signal-to-interference-plus-noise ratios at the SU end are as follows:

[0144]

[0145]

[0146] In equations (17) and (18), T1, T2, T3, and T4 correspond to PU in equation (14). k Desired signal, channel estimation error, multi-user interference and SU interference, T1 SU T2 SU T3 SU These correspond to the SU desired signal, channel estimation error, and PU interference in equation (15), respectively.

[0147] S4.2: Establish the relationship between the power allocation function and the environment-related function.

[0148] Since SU accesses the network as a secondary user, for PU k The interference caused must be less than a certain threshold, i.e., PU k The receiving rate needs to meet R k ≥R0, where R0 is a predefined PU k The receiving rate threshold is then substituted into R (16). k ≥R0 and calculated using channel statistics as the true channel value, we can obtain:

[0149]

[0150] Merge and categorize some variables in equation (19), and rewrite it as follows: with PU k Related environment-related functions and p m The relevant power allocation function f(G,p) m The relational expression:

[0151]

[0152] In equation (20), and f(G,p) m They are respectively:

[0153]

[0154] S4.3: Calculate the minimum number of AP connections M required by SU.

[0155] like Figure 3 The diagram shown is a flowchart illustrating the calculation of the minimum number of AP connections M according to an embodiment of the method of the present invention. The calculation method is as follows:

[0156] S4.3.1: Set the APs The remaining power weight corresponding to each AP is multiplied by its large-scale fading coefficient, and then the results are sorted from largest to smallest to form an original set.

[0157]

[0158] S4.3.2: According to The order of APs in the original AP set The APs in the set are rearranged to obtain the AP set.

[0159] S4.3.3: From a set The first M APs are selected in order to form a set. M starts from 1.

[0160] S4.3.4: Set Substituting the relevant parameters of AP into equation (22), we get:

[0161]

[0162] S4.3.5: Determine whether equation (24) satisfies equation (20). If equation (20) is satisfied, then M+1 and return to S4.3.3. If equation (20) is not satisfied, then the obtained value of M is the minimum number of AP connections required by SU, and output M.

[0163] Step 5: Calculate the optimal power allocation scheme for SU.

[0164] After obtaining the minimum number of AP connections M required by SU, it is necessary to set The calculation involves determining how much power each AP should be allocated to the SU.

[0165] like Figure 4 As shown, the following are the calculation steps for the optimal power allocation scheme of SU according to an embodiment of the method of the present invention:

[0166] S5.1: For the M-1 APs preceding the Mth AP, allocate all remaining power of each AP to the SU.

[0167] S5.2: For the Mth AP, the optimal power allocation is performed using a convex optimization method based on the bisection method, and the steps are as follows:

[0168] S5.2.1: Using f(G,p) m ) M To represent the result of equation (24) when M is taken, the following initial conditions are set, and the calculation starts from n=1:

[0169]

[0170] s0=f(G,p m ) M (26)

[0171] S5.2.2: Determine whether the calculation should continue. Introduce a predefined tolerance ε, ε = 0.01, and then compare ε with... The comparison is based on the following conditions:

[0172]

[0173] If equation (27) is satisfied, it means that the calculation result has reached the optimal power allocation, and jump to S5.2.4. If equation (27) is not satisfied, the optimal power allocation has not yet been reached, and continue to S5.2.3.

[0174] S5.2.3: To reduce the gap between the calculated result and the optimal power allocation at this time, s n Compare with equation (21) as follows:

[0175]

[0176] If equation (28) is satisfied, it means that the calculated result is less than the optimal power allocation, and additional calculations are needed. Let n = n + 1 and Jump to S5.2.2; if equation (28) is not satisfied, it means that the calculated result is greater than the optimal power allocation, and a reduction calculation is needed. Let n = n + 1 and Jump to S5.2.2.

[0177] S5.2.4: Obtain the optimal power allocation calculation result for the Mth AP (p m ) M The calculation method is as follows:

[0178]

[0179] S5.3: After the above steps, the final optimal power allocation scheme for SU can be obtained.

[0180]

Claims

1. A method for allocating power to underlying cognitive users in a cell-free massive MIMO system, characterized in that, In a cellless massive MIMO system area, L access points (APs) with N antennas are randomly distributed, along with K primary users (PUs) and one secondary user (SU). Both the primary and secondary users are single-antenna users. The L>0, N>0, K>0; are used and Let AP and PU be the sets respectively, and AP be the set of PU. l Let PU represent the l-th AP in the set. k This represents the Kth PU in the set; SU, as a single-antenna user that briefly appears in the area, selects the minimum number of APs to connect to after entering the area, using a dynamic set. This represents the selected set of APs, where a certain element is represented by an AP. m To indicate; The method includes the following steps: Step 1, PU k and SU respectively to AP l and AP m A pilot signal is sent, and the pilot signal reaches the AP after being transmitted through the channel; Step 2: First, set up the AP l and AP m The received signal is projected onto and Then, perform minimum mean square error estimation. Step 3, AP l and AP m Perform conjugate precoding on the transmitted signal; Step 4: First, obtain the PU based on the structure of the received signal. k The receiving rate expression for SU is then used to establish the power allocation function. Environment-related functions Relationship: ； Where G represents the large-scale fading coefficient between the AP and the user; Then, the minimum number of AP connections M required by SU is calculated using a relational expression; and They are respectively: ； in, Indicates AP l Assigned to PU k Power weights, Indicates AP m Assigned to PU k’ Power weight, G lk Indicates AP l With PU k Large-scale fading coefficients between; G lk’ Indicates AP l With the k'th main user PU k’ Large-scale fading coefficients between; express The conjugate transpose of . It is the pilot sequence vector of the k'th primary user; Indicates AP l With the kth main user PU k The mean square sum of channel estimates between them Indicates AP l With the k′-th main user PU k′ The mean square sum of channel estimates between; The length of the coherence interval. This refers to the coherence interval length for downlink data transmission. For predefined PU k Receive rate threshold; ； Among them, G mSU Indicates AP m Large-scale fading coefficient between SU ​​and SU It is an intermediate variable substitution symbol; This represents the mean square sum of channel estimates between the m-th AP and the SU; Indicates AP m The power weight assigned to SU, where P represents the maximum normalized transmit power of AP; The calculation process for the optimal power allocation scheme of the SU includes: The calculation process for the minimum number of AP connections M includes: S4.3.

1. Set AP The residual power weight corresponding to each AP is multiplied by its large-scale fading coefficient, and then the results are sorted from largest to smallest to form an original set. : ； S4.3.

2. According to The order of APs in the original AP set The APs in the set are rearranged to obtain the AP set. ; S4.3.

3. From the set The first M APs are selected in order to form a set. M starts from 1; S4.3.

4. Set Substituting the relevant parameters of AP into equation (22), we get: ； S4.3.

5. Determine whether equation (24) satisfies equation (20). If equation (20) is satisfied, then M+1 and return to S4.3.3; if equation (20) is not satisfied, then the obtained value of M is the minimum number of AP connections required by SU, and output M. Step 5: Calculate the optimal power allocation scheme for the SU: After obtaining the minimum number of AP connections M required by the SU, it is necessary to calculate the optimal power allocation scheme for the set. The calculation should determine how much power each AP should be allocated to the SU, including: S5.

1. For the M-1 APs preceding the Mth AP, allocate all remaining power of each AP to SU; S5.

2. For the Mth AP, a convex optimization method based on bisection is used to determine the power of the SU to be allocated until the preset tolerance is met; S5.

3. Output the final power distribution scheme.

2. The underlying cognitive user power allocation method based on a cellless massive MIMO system according to claim 1, characterized in that, In step one, the PU k and SU respectively to AP l and AP m Sending pilot signals, which then travel through the channel to reach the AP, involves the following process: S1.

1. PU k and SU respectively to AP l and AP m Send pilot signal: Using time-division multiplexing, each coherent interval is divided into three parts: uplink training, uplink data transmission, and downlink data transmission, without considering uplink data transmission; assuming... The length of the coherence interval. The uplink training coherence interval length. This refers to the coherence interval length for downlink data transmission. ;PU k and SU respectively to AP l and AP m Send length is pilot sequence , ,in , , , ; S1.

2. The pilot signal arrives at the AP after being transmitted through the channel: The channel model is as follows: ； In the formula, Indicates the first The AP and the first Channel vectors between users Indicates the first The AP and the first Large-scale fading coefficients between individual users Indicates the first The AP and the first The distance between users This represents the path fading impact factor, taking... , Indicates the first The AP and the first The small-scale fading vector among users is The vector, and assume Subject to Rayleigh decay, where each element follows the law of conformity. random variables, This represents a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1. AP l and AP m The signals received by the terminal are as follows: ； ； In equations (2) and (3), The normalized transmit signal-to-noise ratio for each pilot symbol. , For the corresponding received signal The noise matrix, where each element follows a set order. random variables; , They represent AP respectively l To PU k Channels and APs m The channel to SU; , They represent PU k The conjugate transpose of the pilot sequence transmitted by SU.

3. The underlying cognitive user power allocation method based on a cellless massive MIMO system according to claim 1, characterized in that, In step two, the AP is first... l and AP m The received signal is projected onto and Then, the minimum mean square error estimation is performed, which includes the following steps: S2.

1. Will and Projected to and superior: Projection results , They are respectively represented as ； ； S2.

2. Perform minimum mean square error estimation: For the channel and The minimum mean square error (MMSE) estimation is performed, and the estimated value is calculated. and They are respectively: ； ； In equations (6) and (7), This represents the expectation operation. and There are N independent and identical Gaussian components; the mean square sum of the nth component can be obtained from... and express: ； 。 4. The underlying cognitive user power allocation method based on a cellless massive MIMO system according to claim 1, characterized in that, In step three, the AP l and AP m The process of performing conjugate precoding on the transmitted signal includes: AP l To PU k The transmitted signals and AP m The signals sent to SU are respectively ； ； In equations (10) and (11), Indicates AP l Assigned to PU k Power weights, Indicates AP m The power weight assigned to SU, where P represents the maximum normalized transmit power of AP. , for , Conjugate of channel estimation, , Indicates AP l AP m Send to PU k The symbol for SU , .

5. The underlying cognitive user power allocation method based on a cellless massive MIMO system according to claim 1, characterized in that, The specific process of step four includes: S4.

1. Obtain PU based on the structure of the received signal. k The expression for the receiving rate of SU: AP k The received signal and the signal received by SU are respectively ； ； In equations (12) and (13), , , , This represents the transpose of the corresponding channel. , To correspond to additive noise in the received signal, where each element follows a set order. random variables; Equations (12) and (13) can be expanded according to the structure of the signal as follows: ； ； PU k The receiving rate at the SU end can be given by the following formula: ； (16) In the formula, SINR is the signal-to-interference-plus-noise ratio, and PU is the signal-to-interference-plus-noise ratio. k The signal-to-interference-plus-noise ratios at the SU end are as follows: ； ； In equations (17)(18), , , , PU respectively correspond to the formula in (14) k Desired signal, channel estimation error, multi-user interference, and SU interference. , , These correspond to the SU desired signal, channel estimation error, and PU interference in equation (15), respectively. S4.

2. Establish the relationship between the power allocation function and the environment-related function: Since SU accesses the network as a secondary user, for PU k The interference caused must be less than a certain threshold, i.e., PU k The receiving rate needs to meet , For predefined PU k The receiving rate threshold is then substituted into (16). And by using channel statistics as the true value of the channel, we can obtain: ； Merge and categorize some variables in equation (19), and rewrite it as follows: with PU k Related environment-related functions and with Related power allocation functions Relationship: ； In equation (20), and They are respectively: ； ； S4.

3. Calculate the minimum number of AP connections M required by SU.

6. The underlying cognitive user power allocation method based on a cellless massive MIMO system according to claim 1, characterized in that, In step five, the calculation process for the optimal power allocation scheme of the SU includes: S5.

2. For the Mth AP, a convex optimization method based on bisection is used to determine the power allocation of SU until the preset tolerance is met; the specific process is as follows: S5.2.

1. Using To represent the result of equation (24) when M is taken, the following initial conditions are set, and the calculation starts from n=1: ； ； S5.2.

2. Determine whether the calculation should continue, and introduce predefined tolerances. , and will and The comparison is based on the following conditions: ； If equation (27) is satisfied, it means that the calculation result has reached the optimal power allocation, and jump to S5.2.4; if equation (27) is not satisfied, the optimal power allocation has not yet been reached, and continue to S5.2.

3. S5.2.

3. To reduce the difference between the calculated result and the optimal power allocation at this time, Compare with equation (21) as follows: ； If equation (28) is satisfied, it means that the calculated result is less than the optimal power allocation, and additional calculations are needed. Let n = n + 1 and Jump to S5.2.2; if equation (28) is not satisfied, it means that the calculated result is greater than the optimal power allocation, and a reduction calculation is needed. Let n = n + 1 and Jump to S5.2.2; S5.2.

4. Obtain the optimal power allocation calculation result for the Mth AP. Calculation method: ； S5.

3. After the above steps, the final optimal power allocation scheme for SU can be obtained. : 。 7. The underlying cognitive user power allocation method based on a cellless massive MIMO system according to claim 1, characterized in that, The aforementioned cellless massive MIMO system has a defined area of... In a square area, there are 128 randomly distributed access points (APs) (L), 10 antennas (N), 12 primary users (K), and 1 secondary user (1).

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